[ { "id": "authors:g9xxm-58150", "collection": "authors", "collection_id": "g9xxm-58150", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160226-074130931", "type": "article", "title": "A review of fracture in viscoelastic materials", "author": [ { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "abstract": "This review is written in honor of Max L. Williams who not only started this International Journal of Fracture (the author's Ph.D. advisor. Originally the Journal was called International Journal of Fracture Mechanics) but who had a seminally fundamental influence on the course of fracture mechanics in general, and specifically as applied to the time dependent failure of elastomers/polymers. In view of that background this article reviews developments over more than 50 years, as colored by my own experiences in regard to this topic. It seems appropriate to include a historical perspective that starts during pre-journal times and addresses the need for understanding time dependent processes governing fracture in rate sensitive materials. To the largest extent, the rate dependence is important where polymers are involved, though under more limited conditions metals and igneous solids as well as ligneous ones exhibit time dependent fracture characteristics. Such facts notwithstanding, the major discussion in this contribution is devoted here to the time dependent fracture of polymeric materials, and elastomeric ones in particular. The emphasis will be thus on time dependent issues governed primarily by the fracture processes in elastomeric solids, which have evolved largely in parallel to problems devoted to the more rigid polymers. Because consideration of fracture of the rigid polymers has often, if not usually, minimized the time dependence, only cursory attention is paid to these, in spite of the fact that they constitute a very important class of materials in the modern engineering community. From an engineering perspective this review is motivated also by an exposition of a persistent lack of knowledge concerning time dependent fracture issues. Most of the work attached to the notion of viscoelastic fracture is\u2014intentionally or by omission\u2014associated with the phenomenon of crack growth under steady state conditions with the expectation that this understanding leads implicitly to resolution of problems governed by transient loadings. Besides reviewing the historical evolution of the knowledge in this field over the past half century, it is a main purpose of this paper to offer information that has either been ignored or has not been explored (this includes the work of the author), but which contradicts this \"popular\" perception. It is thus an intentionally large part of this presentation which documents compelling motivation for addressing fracture aspects, that are generally important from an engineering design and analysis point-of-view: specifically, it is intended to illustrate the remarkable degree by which the steady state solution to crack propagation deviates from experimental information when transient conditions prevail, and the large range of time scales over which this failure behavior is observed.", "doi": "10.1007/s10704-015-0058-6", "issn": "0376-9429", "publisher": "Springer", "publication": "International Journal of Fracture", "publication_date": "2015-11", "series_number": "1-2", "volume": "196", "issue": "1-2", "pages": "99-146" }, { "id": "authors:ab5wb-1bj30", "collection": "authors", "collection_id": "ab5wb-1bj30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150416-154211473", "type": "article", "title": "In Memoriam Max Lea Williams (February 22, 1922-September 18, 2013)", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "A seminal mind has departed: His students and the whole engineering community shall miss a concerned, rational engineer and scientist, whose actions were broadly based in the desire to improve the world in which we live. Though M. L. Williams was associated with academic institutions throughout his career, he demonstrated a firm belief in practical, hands-on engineering. He was a Registered Engineer and had a major influence in guiding national programs of defense research, saving millions of dollars through judiciously supporting, criticizing or phasing studies and programs. His practical insights transitioned into engineering management through guidance of (over 20) start-up engineering ventures, which depended critically on mature engineering judgment and the teaching by his economics mentor Economics Professor Horace Gilbert while a graduate student at Caltech.", "doi": "10.1007/s10704-015-0008-3", "issn": "0376-9429", "publisher": "Springer", "publication": "International Journal of Fracture", "publication_date": "2015-02", "series_number": "1-2", "volume": "191", "issue": "1-2", "pages": "9-11" }, { "id": "authors:rtzbs-ypj97", "collection": "authors", "collection_id": "rtzbs-ypj97", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200520-074532493", "type": "book_section", "title": "Experimental Investigation of Failure in Viscoelastic Elastomers Under Combined Shear and Pressure", "book_title": "Challenges in Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials", "author": [ { "family_name": "Alkhader", "given_name": "Maen", "clpid": "Alkhader-M" }, { "family_name": "Knauss", "given_name": "Wolfgang", "clpid": "Knauss-W-G" }, { "family_name": "Ravichandran", "given_name": "Guruswami", "orcid": "0000-0002-2912-0001", "clpid": "Ravichandran-G" } ], "contributor": [ { "family_name": "Antoun", "given_name": "Bonnie", "clpid": "Antoun-B" }, { "family_name": "Qi", "given_name": "H. Jerry", "clpid": "Qi-H-Jerry" }, { "family_name": "Hall", "given_name": "Richard", "clpid": "Hall-Richard" }, { "family_name": "Tandon", "given_name": "G. P.", "clpid": "Tandon-G-P" }, { "family_name": "Lu", "given_name": "Hongbing", "clpid": "Lu-Hongbing" }, { "family_name": "Lu", "given_name": "Charles", "clpid": "Lu-Charles" } ], "abstract": "An experimental approach, based on Split Hopkinson Pressure Bar (SHPB) apparatus, is developed to elucidate failure of viscoelastic elastomers under combined shear and high pressures such as are encountered in explosive and/or armor-impact scenarios. In this experimental arrangement, thin cylindrical polyurea specimens with an aspect ratio (Diameter to thickness) greater or equal to 15 are tested, up to failure, using Split Hopkinson Pressure Bar (SHPB). Specimens with large aspect ratio are used to guarantee the close approximation of a triaxial state of stress in the specimen upon loading; hence the measured normal stress would be approximately equal to the hydrostatic pressure in the specimen. Friction at the loading interfaces forces the stress state to deviate from uniformity, restrict both the circumferential and radial displacements and lead to the development of shear stresses and strains. Hence, induced failure occurs under conditions combining high-strain-rate, high pressure and shear stresses. By using this setup, repeatable failure modes were detected and elucidated using finite element simulations.", "doi": "10.1007/978-1-4614-4241-7_8", "isbn": "978-1-4614-4240-0", "publisher": "Springer", "place_of_publication": "New York, NY", "publication_date": "2013-10-25", "pages": "55-62" }, { "id": "authors:fmyy4-pgm02", "collection": "authors", "collection_id": "fmyy4-pgm02", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121015-121832397", "type": "article", "title": "A New Shear-Compression Test for Determining the Pressure\n Influence on the Shear Response of Elastomers", "author": [ { "family_name": "Alkhader", "given_name": "M.", "clpid": "Alkhader-M" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Ravichandran", "given_name": "G.", "orcid": "0000-0002-2912-0001", "clpid": "Ravichandran-G" } ], "abstract": "A new shear-compression experiment for investigating\nthe influence of hydrostatic pressure (mean stress)\non the large deformation shear response of elastomers is\npresented. In this new design, a nearly uniform torsional\nshear strain is superposed on a uniform volumetric\ncompression strain generated by axially deforming specimens\nconfined by a stack of thin steel disks. The new\ndesign is effective in applying uniform shear and multiaxial\ncompressive stress on specimens while preventing buckling\nand barreling during large deformation under high loads.\nBy controlling the applied pressure and shear strain\nindependently of each other, the proposed setup allows for\nmeasuring the shear and bulk response of elastomers at\narbitrary states within the shear-pressure stress space.\nThorough evaluation of the new design is conducted via\nlaboratory measurements and finite element simulations.\nPractical issues and the need for care in specimen\npreparation and data reduction are explained and discussed.\nThe main motivation behind developing this setup is to aid\nin characterizing the influence of pressure or negative\ndilatation on the constitutive shear response of elastomeric\ncoating materials in general and polyurea in particular.\nExperimental results obtained with the new design illustrate\nthe significant increase in the shear stiffness of polyurea\nunder moderate to high hydrostatic pressures.", "doi": "10.1007/s11340-011-9572-2", "issn": "0014-4851", "publisher": "Springer", "publication": "Experimental Mechanics", "publication_date": "2012-10", "series_number": "8", "volume": "52", "issue": "8", "pages": "1151-1161" }, { "id": "authors:a2b6t-8qa95", "collection": "authors", "collection_id": "a2b6t-8qa95", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120518-095654000", "type": "article", "title": "On the importance of the dilatational component of the stress state in the uniaxial yield-like behavior of rate-dependent polymers: C. Bauwens-Crowet revisited", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "The effect of the dilatational stress component on the yield-like behavior of ratedependent polymers is examined via the example of PMMA. Starting with uniaxial data\npublished in 1973 by C. Bauwens-Crowet and describing the dependence of yield (maximum) stress in compression and in tension, the then offered reduction or \"shift\" scheme\nis reviewed, in particular the fact that tension and compression data lead to different data reductions. Following the argument that mechanically induced dilatation can affect the time dependence of polymeric deformation processes much like temperature affects temporal scaling, the same data is then subjected to an analysis based on volumetric changes accompanying mechanical loading. It is found that such a treatment unifies the compression and\ntension data into a single master curve to the extent that temperature and loads from the two deformation modes are congruous and exhibit no more data scatter than the presentation of the original data reduction. Moreover, the time\u2013temperature shift properties for this newly reduced yield-like behavior then follows also the same rules and properties as do viscoelastic mechanical properties acquired under small deformations.", "doi": "10.1007/s11043-011-9149-6", "issn": "1385-2000", "publisher": "Springer", "publication": "Mechanics of Time-Dependent Materials", "publication_date": "2012-05", "series_number": "2", "volume": "16", "issue": "2", "pages": "223-240" }, { "id": "authors:5hy1m-90013", "collection": "authors", "collection_id": "5hy1m-90013", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120104-162619503", "type": "article", "title": "A note on the role of dilatation in the fracture of viscoelastic elastomer", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "Fracture models addressing crack propagation in viscoelastic materials typically draw on cohesive force distributions coupled with a linearly viscoelastic constitutive material description. While the resulting formulation of the crack speed as a function of applied loads provides good agreement with measurements on polyurethane rubber as well as three other rubbery solids studied by A. N. Gent on the more global scale, the size of the cohesive zone required to match theory and measurements is unreasonably small. Although this glaring discrepancy has not deterred the use of the theory for viscoelastic fracture, it has remained a troublesome question on the wider applications to polymer fracture. The present note revisits this issue and draws on results developed during the past decade to explain this discrepancy via the effect\nof stress-induced dilatation on the relaxation or retardation times of viscoelastic solids.", "doi": "10.1007/s10704-011-9629-3", "issn": "0376-9429", "publisher": "Springer", "publication": "International Journal of Fracture", "publication_date": "2011-10", "series_number": "2", "volume": "171", "issue": "2", "pages": "99-104" }, { "id": "authors:nt0d1-wam47", "collection": "authors", "collection_id": "nt0d1-wam47", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200520-144612061", "type": "book_section", "title": "Experimental arrangement for measuring the high-strain-rate response of polymers under pressures", "book_title": "Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials", "author": [ { "family_name": "Alkhader", "given_name": "Maen", "clpid": "Alkhader-M" }, { "family_name": "Knauss", "given_name": "Wolfgang", "clpid": "Knauss-W-G" }, { "family_name": "Ravichandran", "given_name": "Guruswami", "orcid": "0000-0002-2912-0001", "clpid": "Ravichandran-G" } ], "contributor": [ { "family_name": "Proulx", "given_name": "Tom", "clpid": "Proulx-T" } ], "abstract": "This study aims to investigate the high-strain-rate shear response of viscoelastic elastomeric coatings at large strains and under elevated levels of hydrostatic pressure. Results of this study shed light on the combined effects of deformation rate and pressure which might promote a transition from viscoelastic to glassy behavior. This work utilizes a Split Hopkinson Pressure Bar (SHPB) apparatus in conjunction with a customized version of the recently proposed Shear Compression Specimen (SCS) which consists of a polymer gage section with two metal ends that remain essentially rigid during deformation. Detailed finite element simulations were used to customize the adopted specimen, to determine its proper dimensions and promote its functionality. The customized specimen permits subjecting the tested specimen to a state of uniform pressure and shear stress, while allowing for measuring pressure, shear stress and shear strain directly. Results obtained using the customized specimen, which are included in this paper, illustrate its usefulness in measuring the effect of high-strain-rate, large strain and hydrostatic pressure on the shear stress-strain response of viscoelastic elastomers.", "doi": "10.1007/978-1-4614-0213-8_20", "isbn": "978-1-4614-0212-1", "publisher": "Springer", "place_of_publication": "New York, NY", "publication_date": "2011-05-11", "pages": "139-144" }, { "id": "authors:mttpk-ken14", "collection": "authors", "collection_id": "mttpk-ken14", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200601-143119734", "type": "book_section", "title": "The influence of pressure on the large deformation shear response of a Polyurea", "book_title": "Time Dependent Constitutive Behavior and Fracture/Failure Processes", "author": [ { "family_name": "Alkhader", "given_name": "Maen", "clpid": "Alkhader-M" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Ravichandran", "given_name": "G.", "orcid": "0000-0002-2912-0001", "clpid": "Ravichandran-G" } ], "contributor": [ { "family_name": "Proulx", "given_name": "Tom", "clpid": "Proulx-T" } ], "abstract": "A new shear-compression experiment is developed to characterize the influence of hydrostatic pressure on the shear constitutive response of nearly incompressible viscoelastic materials undergoing large deformations. In this design, a uniform torsional shear stress is superposed on a uniform hydrostatic compressive state of stress generated by axially deforming samples confined by a stack of thin steel disks. The new design is effective in applying uniform multiaxial compressive strain while preventing buckling and barreling during inelastic deformation. In addition, it allows for the direct measurement of the stress and strain fields during the deformation history. The new shear-compression setup is developed to aid in characterizing the influence of pressure or negative dilatation on the shear constitutive response of viscoelastic materials in general and Polyurea in particular. Experimental results obtained with this technique illustrate the significant increase in the shear stiffness of polyurea under moderate to high hydrostatic pressures.", "doi": "10.1007/978-1-4419-9794-4_40", "isbn": "978-1-4419-9498-1", "publisher": "Springer", "place_of_publication": "New York, NY", "publication_date": "2011-04-15", "pages": "287-295" }, { "id": "authors:bjhwx-bny29", "collection": "authors", "collection_id": "bjhwx-bny29", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090812-093155591", "type": "article", "title": "A new shear-compression-specimen for determining quasistatic and dynamic polymer properties", "author": [ { "family_name": "Zhao", "given_name": "J.", "clpid": "Zhao-J" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Ravichandran", "given_name": "G.", "orcid": "0000-0002-2912-0001", "clpid": "Ravichandran-G" } ], "abstract": "A new design of the shear compression specimen (SCS) for investigating the viscoelastic shear response of polymers is presented. The specimen consists of a polymer gage section with two metal ends that remain essentially rigid during deformation. Two closed-form analytic models are developed to predict the average stress and strain in the gage section from the deformation-load histories. This new SCS design and its analytic models are thoroughly evaluated via laboratory measurements and numerical simulations. These simulations show that the deformations in the gage section are more uniform than in the original design, and the distribution of the average shear stress and strain are highly homogenous. The simulation results yield good agreement with those of closed-form analytic results and the experiments demonstrate that the new SCS geometry and its analytic models are as reliable as other commonly employed specimens. It can also generate higher strain rates under usual loading conditions because of its smaller specimen gage length. The need for care in specimen preparation is also discussed in detail as illuminated by the experimental and simulation results.", "doi": "10.1007/s11340-008-9171-z", "issn": "0014-4851", "publisher": "Springer", "publication": "Experimental Mechanics", "publication_date": "2009-06", "series_number": "3", "volume": "49", "issue": "3", "pages": "427-436" }, { "id": "authors:rze2b-9e802", "collection": "authors", "collection_id": "rze2b-9e802", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:ZHAmtdm07", "type": "article", "title": "Applicability of the time\u2013temperature superposition principle in modeling dynamic response of a polyurea", "author": [ { "family_name": "Zhao", "given_name": "J.", "clpid": "Zhao-J" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Ravichandran", "given_name": "G.", "orcid": "0000-0002-2912-0001", "clpid": "Ravichandran-G" } ], "abstract": "This paper addresses the applicability of the Time\u2013Temperature Superposition Principle in the dynamic response of a polyurea polymer at high strain rates and different temperatures. Careful and extensive measurements in the time domain of the relaxation behavior and subsequent deduction of a master-relaxation curve establish the mechanical behavior for quasistatic deformations over a time range of 16 decades. To examine its validity in a highly dynamic environment, experiments with the aid of a split Hopkinson (Kolsky) pressure bar are carried out. The use of a two-material pulse shaper allows for stress equilibrium across the specimen during the compression process, to concentrate on the initial, small deformation part that characterizes linearly viscoelastic behavior. This behavior of polyurea at high strain rates and different temperatures is then investigated by comparing results from a physically fully three-dimensional (axisymmetric) numerical model, employing the quasistatically obtained properties, with corresponding Hopkinson bar measurements. The experimentally determined wave history entering the specimen is used as input to the model. Experimental and simulation results are compared with each other to demonstrate that the Time\u2013Temperature Superposition Principle can indeed provide the requisite data for high strain rate loading of viscoelastic solids, at least to the extent that linear viscoelasticity applies with respect to the polyurea material.", "doi": "10.1007/s11043-008-9048-7", "issn": "1385-2000", "publisher": "Springer", "publication": "Mechanics of Time-Dependent Materials", "publication_date": "2007-12", "series_number": "3-4", "volume": "11", "issue": "3-4", "pages": "289-308" }, { "id": "authors:w7cx8-m4858", "collection": "authors", "collection_id": "w7cx8-m4858", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KNAjap04", "type": "article", "title": "Pressure-sensitive dissipation in elastomers and its implications for the detonation of plastic explosives", "author": [ { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" }, { "family_name": "Sundaram", "given_name": "Sairam", "clpid": "Sundaram-S" } ], "abstract": "The role of binder deformation and the associated energy dissipation on the detonation sensitivity of plastically bonded explosives is considered by accounting for dilatation-sensitive viscoelastic shear response. Following the observation that pressurization can prolong the relaxation and retardation times of a viscoelastic elastomer tremendously, the implications of this phenomenon are considered for a thin layer of a model elastomer, sheared between two blocks of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine under deformation rates typical in detonation scenarios. The consequences of concurrent pressurization on heat generation are examined using small deformation as well as finite deformation analyses. While a dilatation-insensitive viscoelastic behavior generates notable temperature increases, they are insufficient to cause ignition of the explosive. However, taking into account the increased dissipation associated with the pressure-induced changes in the intrinsic time scale and viscosity of the elastomer leads to temperature rises on the order of 1000degreesC, which are consistent with \"hot spots\" held responsible for the initiation of detonation in the adjacent explosive grains.", "doi": "10.1063/1.1818349", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "2004-12-15", "series_number": "12", "volume": "96", "issue": "12", "pages": "7254-7266" }, { "id": "authors:9109z-rxa53", "collection": "authors", "collection_id": "9109z-rxa53", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191028-152259537", "type": "article", "title": "The mechanical strength of polysilicon films: Part 1. The influence of fabrication governed surface conditions", "author": [ { "family_name": "Chasiotis", "given_name": "Ioannis", "orcid": "0000-0001-6521-8332", "clpid": "Chasiotis-Ioannis" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "abstract": "In an effort to explain the considerable variations in measured mechanical strength of polysilicon films doped with phosphorous for use in MEMS applications, the influence of the specimen manufacturing processes on the mechanical properties has been examined in connection with varying exposure to 49% hydrofluoric acid (HF). It was found that surface roughness as characterized by groove formation along grain boundaries depends on the HF release time. Surface undulations and crevasses related to grain structure result thus in reduced fracture strength and, in addition, induce errors into the determination of the effective elastic modulus\u2014especially when the latter is determined from flexure configurations. Extensive exposure to HF results in pervasive material degradation, as evidenced by a transition from transgranular to intergranular fracture, and a correspondingly precipitous drop of the film strength with attendant increase in grain boundary material removal. Short times of exposure to HF can result in delamination of a thin surface layer, which is sufficient to initiate an \"early\" failure. Longer exposure allows HF permeation into the intergranular domains, degrading the body of the material significantly. On the other hand, tests on material from a different source that has undergone different doping and post-processing demonstrated a suppression of this degradation resulting in film strengths that are higher by a factor of two or more. Thus, consideration of additional influences of doping and electro-chemical phenomena during the HF wet release, in association with silicon-metal contacts, is necessary.", "doi": "10.1016/S0022-5096(03)00051-6", "issn": "0022-5096", "publisher": "Elsevier", "publication": "Journal of the Mechanics and Physics of Solids", "publication_date": "2003-08", "series_number": "8", "volume": "51", "issue": "8", "pages": "1533-1550" }, { "id": "authors:6rd1h-jzv06", "collection": "authors", "collection_id": "6rd1h-jzv06", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CHAjmps03b", "type": "article", "title": "The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular perforations", "author": [ { "family_name": "Chasiotis", "given_name": "Ioannis", "orcid": "0000-0001-6521-8332", "clpid": "Chasiotis-Ioannis" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "abstract": "A systematic study of failure initiation in small-scale specimens has been performed to assess the effect of size scale on \"failure properties\" by drawing on the classical analysis of elliptically perforated specimens. Limitations imposed by photolithography restricted the minimum radii of curvature of the specimen perforations to one micron. By varying the radius of curvature and the size of the ellipses, the effects of domain size and stress concentration amplitude could be assessed separately to the point where the size of individual grains (~0.3 \u00b5m) becomes important. The measurements demonstrate a strong influence of the domain size under elevated stress on the \"failure strength\" of MEMS scale specimens, while the amplitude, or the variation, of the stress concentration factor is less significant. In agreement with probabilistic considerations of failure, the \"local failure strength\" at the root of a notch clearly increases as the radius of curvature becomes smaller. Accordingly, the statistical scatter also increases with decreasing size of the (super)stressed domain. When the notch radius becomes as small as 1 \u00b5m the failure stress increases on average by a factor of two relative to the tension values derived from unnotched specimens. This effect becomes moderate for larger radii of curvature, up to a radius of 8 \u00b5m (25 times the grain size), for which the failure stress at the notch tip closely approaches the value of the tensile strength for un-notched tensile configurations. We deduce that standard tests, performed on micron-sized, non-perforated, tension specimens, provide conservative strength values for design purposes. In addition, a Weibull analysis shows for surface-micromachined specimens a dependence of the strength on the specimen length, rather than the surface area or volume, which implies that the sidewall geometry, dimensions and surface conditions can dominate the failure process.", "doi": "10.1016/S0022-5096(03)00050-4", "issn": "0022-5096", "publisher": "Elsevier", "publication": "Journal of the Mechanics and Physics of Solids", "publication_date": "2003-08", "series_number": "8", "volume": "51", "issue": "8", "pages": "1551-1572" }, { "id": "authors:e0bwd-gs488", "collection": "authors", "collection_id": "e0bwd-gs488", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191008-142521434", "type": "article", "title": "Scaling global fracture behavior of structures-sized laminated composites", "author": [ { "family_name": "Gonz\u00e1les", "given_name": "Luis", "clpid": "Gonz\u00e1les-L" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "abstract": "The propagation of damage in laminated fiber composites similar to a crack-like configuration is studied experimentally. Of particular interest is the behavior of a 'macro-crack' or 'global crack' that propagates through a large scale structure (e.g., airplane fuselage or wing) with the potential interaction of stringers or other reinforcements. The question is considered whether such damage propagation can be understood in terms of classical fracture mechanics. Because the damage zone (wake width) can be very extensive and may be measured in terms of inches, the question arises as to the scalability of associated 'fracture' phenomena. An integral part of this investigation is thus an examination of the size of the test specimens to establish whether a minimum size is required to relate fracture at larger scales by laboratory specimens. Using (globally anisotropic) 32-lamina composite specimens, proportioned like compact tension specimens, it is found that test 'coupons' on the order of 45 to 50 cm on a side (18\u00d718 in.^2) or larger are needed to begin simulating large scale structures for establishing a global equivalent of a fracture energy for 'crack propagation' simulations. Displacement controlled tests on groups of three specimen sizes (15, 30 and 46 cm on a side) indicate that scaling can be accomplished through the square root of the linear specimen or crack dimension. In certain lay-ups 'run-away delamination' severs the surface laminae so that the reinforcement action of stringers is jeopardized. Damage at the `global crack front' is quantified through an effective area relation, with a characteristic value for the mostly intra-laminar initiation of damage (intra-lamina cracks) at a sharp notch, and another value conceived of as governing the onset of unstable growth.", "doi": "10.1023/a:1023351115322", "issn": "0376-9429", "publisher": "Springer", "publication": "International Journal of Fracture", "publication_date": "2002-12", "series_number": "4", "volume": "118", "issue": "4", "pages": "363-394" }, { "id": "authors:s9rf6-4zt20", "collection": "authors", "collection_id": "s9rf6-4zt20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200221-155049786", "type": "article", "title": "Nonlinearly Viscoelastic Behavior of Polycarbonate. II. The Role of Volumetric Strain", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Zhu", "given_name": "W.", "clpid": "Zhu-W" } ], "abstract": "The creep responses of (bisphenol A) polycarbonate at 80\u00b0C undercombined two-dimensional shear with superposed tensile and compressivestress states were measured on Arcan specimens in the nonlinearlyviscoelastic regime. Of particular interest is the influence of thedilatational deformation component on the nonlinearly viscoelastic creepbehavior. Because the nonlinear material response determines the stressdistribution under fixed deformation or load, but is not known a priori,a re-estimation of the latter is essential to verify or adjust thestress state(s). This is accomplished by approximating isochronalstress-strain relations derived from shear creep behavior, encompassingthe nonlinear domain, by a classical incremental elasto-plastic materialdescription at appropriate times. To the extent that the two-dimensionalcharacter of the test configuration permits accessing three-dimensionalinformation, a coherent representation of the results is examined interms of maximum shear and/or octahedral representation.\n\nIt is found that the creep behavior under shear and normal stressor deformation imposition differ significantly: When viewed as aresponse to the imposition of a maximum shear stress, the creepresponses differ depending on whether one or the other dominates. On theother hand, if the response is formulated in terms of an octahedraldescription the representation becomes less sensitive to normal vs.shear behavior. It is clear in either case, however, that normal strainhas a disproportionately large effect on creep response in shear. Withinthe precision underlying the measurements it is found that the shear andnormal strain components accumulate under creep in nearly constantratios. Under this scenario it is demonstrated clearly that theinfluence of negative dilatational stress (or deformation) on pure sheardeformation leads to distinctly lower creep rates. The converse is true,if positive dilatational stresses are added, though not monotonically so.", "doi": "10.1023/a:1021296110580", "issn": "1385-2000", "publisher": "Springer", "publication": "Mechanics of Time-Dependent Materials", "publication_date": "2002-12", "series_number": "4", "volume": "6", "issue": "4", "pages": "301-322" }, { "id": "authors:aqykr-2d041", "collection": "authors", "collection_id": "aqykr-2d041", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190826-124739024", "type": "article", "title": "The Effect of Temperature and Pressure on the Mechanical Properties of Thermo- and/or Piezorheologically Simple Polymeric Materials in Thermodynamic Equilibrium \u2013 A Critical Review", "author": [ { "family_name": "Tschoegl", "given_name": "N. W.", "clpid": "Tschoegl-N-W" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" }, { "family_name": "Emri", "given_name": "Igor", "clpid": "Emri-I" } ], "abstract": "The mechanical properties of polymeric materials quite generally dependon time, i.e., on whether they are deformed rapidly or slowly. The timedependence is often remarkably large. The complete description of themechanical properties of a polymeric material commonly requires thatthey be traced through 10, 15, or even 20 decades of time. The class ofpolymeric materials referred to as thermorheologically and/orpiezorheologically simple materials allows use of the superposition ofthe effects of time and temperature and/or time and pressure in suchmaterials as a convenient means for extending the experimental timescale.\n\nThis paper presents a critical review of models proposed todescribe the effect of temperature and/or pressure on time-dependent thermorheologically and/or piezorheologically simple polymericmaterials. The emphasis here is on the theoretical aspects, although experimental results are used as illustrations wherever appropriate.", "doi": "10.1023/a:1014421519100", "issn": "1385-2000", "publisher": "Springer", "publication": "Mechanics of Time-Dependent Materials", "publication_date": "2002-03", "series_number": "1", "volume": "6", "issue": "1", "pages": "53-99" }, { "id": "authors:rmbmy-7bt05", "collection": "authors", "collection_id": "rmbmy-7bt05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191008-150952468", "type": "article", "title": "Poisson's Ratio in Linear Viscoelasticity \u2013 A Critical Review", "author": [ { "family_name": "Tschoegl", "given_name": "N. W.", "clpid": "Tschoegl-N-W" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" }, { "family_name": "Emri", "given_name": "Igor", "clpid": "Emri-I" } ], "abstract": "Poisson's ratio is an elastic constant defined as the ratio of thelateral contraction to the elongation in the infinitesimal uniaxialextension of a homogeneous isotropic body. In a viscoelastic materialPoisson's ratio is a function of time (or frequency) that depends on thetime regime chosen to elicit it. It is important as one of the materialfunctions that characterize bulk behavior.\n\nThis paper develops the linear theory of the time- orfrequency-dependent Poisson's ratio, and it reviews work on itsexperimental determination. The latter poses severe difficulties in viewof the high accuracy required. Thus, reliable information on theviscoelastic Poisson's ratio is as yet rather scanty.\n\nThe paper also reports on attempts to measure the Poisson's ratioof a viscoelastic material as a function of temperature. Lateralcontraction in creep and at constant rate of extension receivesattention as well.", "doi": "10.1023/a:1014411503170", "issn": "1385-2000", "publisher": "Springer", "publication": "Mechanics of Time-Dependent Materials", "publication_date": "2002-03", "series_number": "1", "volume": "6", "issue": "1", "pages": "3-51" }, { "id": "authors:f8d3n-r8v05", "collection": "authors", "collection_id": "f8d3n-r8v05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CHAem02", "type": "article", "title": "A New Microtensile Tester for the Study of MEMS Materials with the Aid of Atomic Force Microscopy", "author": [ { "family_name": "Chasiotis", "given_name": "Ioannis", "orcid": "0000-0001-6521-8332", "clpid": "Chasiotis-Ioannis" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "abstract": "An apparatus has been designed and implemented to measure the elastic tensile properties (Young's modulus and tensile strength) of surface micromachined polysilicon specimens. The tensile specimens are \"dog-bone\" shaped ending in a large \"paddle\" for convenient electrostatic or, in the improved apparatus, ultraviolet (UV) light curable adhesive gripping deposited with electrostatically controlled manipulation. The typical test section of the specimens is 400 \u00b5m long with 2 \u00b5m x 50 \u00b5m cross section. The new device supports a nanomechanics method developed in our laboratory to acquire surface topologies of deforming specimens by means of Atomic Force Microscopy (AFM) to determine (fields of) strains via Digital Image Correlation (DIC). With this tool, high strength or non-linearly behaving materials can be tested under different environmental conditions by measuring the strains directly on the surface of the film with nanometer resolution.", "doi": "10.1007/BF02411051", "issn": "0014-4851", "publisher": "Springer", "publication": "Experimental Mechanics", "publication_date": "2002-03", "series_number": "1", "volume": "42", "issue": "1", "pages": "51-57" }, { "id": "authors:bsfkn-cd041", "collection": "authors", "collection_id": "bsfkn-cd041", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191008-111635947", "type": "article", "title": "On Interconversion of Various Material Functions of PMMA", "author": [ { "family_name": "Sane", "given_name": "S. B.", "clpid": "Sane-S-B" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "The interconversion between various linear viscoelastic functions for Poly (methyl) methacrylate (PMMA) is explored. With the availability of four time or frequency-dependent material functions (shear, bulk, uniaxial and Poisson) on the same material, various material functions are computed using the correspondence principle of the linearized theory of viscoelasticity through the use of standard relations. Computed material functions are evaluated against the directly measured properties and the limitations imposed on successful interconversion due to the experimental errors in the underlying physical data are explored.It is observed that the differences between the computed and measured functions were larger than suggested by experimental error. The results intimates the need to thoroughly re-examine the applicability of time-temperature superposition principle often employed to develop 'master curves' for viscoelastic functions, especially with respect to the glassy domain.", "doi": "10.1023/a:1012586719210", "issn": "1385-2000", "publisher": "Springer", "publication": "Mechanics of Time-Dependent Materials", "publication_date": "2001-12", "series_number": "4", "volume": "5", "issue": "4", "pages": "325-343" }, { "id": "authors:abgzz-k3a65", "collection": "authors", "collection_id": "abgzz-k3a65", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190816-144341444", "type": "article", "title": "Molecular dynamics simulations to compute the bulk response of amorphous PMMA", "author": [ { "family_name": "Sane", "given_name": "Sandeep B.", "clpid": "Sane-S-B" }, { "family_name": "\u00c7a\u011fin", "given_name": "Tahir", "orcid": "0000-0002-3665-0932", "clpid": "\u00c7a\u011fin-T" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" }, { "family_name": "Goddard", "given_name": "William A., III", "orcid": "0000-0003-0097-5716", "clpid": "Goddard-W-A-III" } ], "abstract": "The results of molecular dynamics computations and corresponding values of laboratory measurements are compared to assess the efficacy of the numerical method. Details are presented on the modeling process, including the selection of an appropriate force field derived from separate computations on isotactic (crystalline) PMMA together with commensurate experimental data. It is found that in addition to typical energy minimization and temperature annealing cycles to establish equilibrium models, it is advantageous to also subject the model samples to a cycle of a relatively large pressure excursion (GPa's), to further improve the equilibrium state. Although the computations are limited to small samples in a physical sense (three polymer chains with fifty monomer units per chain per unit cell containing 2256 atoms), it appears that the primary limitation of the comparison with experimental data rests in the very short times (picoseconds). Estimates based on the time-temperature superposition principle do not overcome this difficulty, but may, on the other hand, signify limitations of the time-temperature trade-off as normally practiced.", "doi": "10.1023/a:1020042716635", "issn": "0928-1045", "publisher": "Springer", "publication": "Journal of Computer-Aided Materials Design", "publication_date": "2001-05", "series_number": "2/3", "volume": "8", "issue": "2/3", "pages": "87-106" }, { "id": "authors:asy7m-a7e51", "collection": "authors", "collection_id": "asy7m-a7e51", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181204-132724650", "type": "book_section", "title": "Microtensile tests with the aid of probe microscopy for the study of MEMS materials", "book_title": "Materials and Device Characterization in Micromachining III", "author": [ { "family_name": "Chasiotis", "given_name": "Ioannis", "orcid": "0000-0001-6521-8332", "clpid": "Chasiotis-Ioannis" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "contributor": [ { "family_name": "Vladimirsky", "given_name": "Yuli", "clpid": "Vladimirsky-Y" }, { "family_name": "Coane", "given_name": "Philip J.", "clpid": "Coane-P-J" } ], "abstract": "Mechanical tests of thin films require novel and sophisticated methods that can address the geometry and microstructure of the films. A new method of micro-tensile testing of MicroElectroMechanical Systems (MEMS) films has been demonstrated. An improved apparatus has been designed and implemented to measure the elastic tensile properties. (Young's modulus, Poisson's ration and tensile strength) of surface micromachined polysilicon specimans. The tensile specimans are dog-bone shaped ending in a large paddle for convenient electrostatic or, in the improved apparatus, UV adhesive gripping. The test section of the specimens is 400\u00b5m long with 2\u00b5mx50\u00b5m cross section. The method employs Atomic Force Microscope (AFM) acquired surface topologies of deforming specimans to determine (fields of) strain by way of the Digital Image Correlation method (DIC). With this method, high strength of non- linearly behaving materials under different environmental conditions can be tested by measuring the strains directly on the surface of the film with nanometer resolution in in-place and out-of-plane measurements.", "doi": "10.1117/12.395616", "isbn": "9780819438317", "publisher": "Society of Photo-optical Instrumentation Engineers (SPIE)", "place_of_publication": "Bellingham, WA", "publication_date": "2000-08-11", "pages": "96-103" }, { "id": "authors:71ch1-enn68", "collection": "authors", "collection_id": "71ch1-enn68", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190826-124739257", "type": "article", "title": "A Note on the Determination of Relaxation and Creep Data from Ramp Tests", "author": [ { "family_name": "Lee", "given_name": "S.", "clpid": "Lee-S" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "The response of (linearly) viscoelastic material is approximately the same for ramp and true step strain histories once an initial time interval of about ten times the ramp-up time has passed.Because the loss of relaxation data during that initial time can be a substantial portion of the total (logarithmically measured) time scale, a simple method is documented for exploiting data obtained from the initial ramp history via a recursion formula. Comparison of data obtained in ramp and relaxation histories are demonstrated to yield good results within the accuracy of the test method.", "doi": "10.1023/a:1009827622426", "issn": "1385-2000", "publisher": "Springer", "publication": "Mechanics of Time-Dependent Materials", "publication_date": "2000-03", "series_number": "1", "volume": "4", "issue": "1", "pages": "1-7" }, { "id": "authors:rbwrz-m0881", "collection": "authors", "collection_id": "rbwrz-m0881", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180813-091037460", "type": "book_section", "title": "Mechanical properties of thin polysilicon films by means of probe microscopy", "book_title": "Materials and Device Characterization in Micromachining", "author": [ { "family_name": "Chasiotis", "given_name": "Ioannis", "orcid": "0000-0001-6521-8332", "clpid": "Chasiotis-Ioannis" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "contributor": [ { "family_name": "Friedrich", "given_name": "Craig R.", "clpid": "Friedrich-C-R" }, { "family_name": "Vladimirsky", "given_name": "Yuli", "clpid": "Vladimirsky-Y" } ], "abstract": "A new method for tensile testing of thin films is being developed. An electrostatic grip apparatus was designed and implemented to measure the elastic and ultimate tensile properties (Young's modulus, Poisson's ratio and tensile strength) of surface micromachined polysilicon specimens. The tensile specimens are 'dog-bone' shaped ending in a large 'paddle' for electrostatic gripping. The test section of the specimens is 400 micrometers long and with 2 micrometer X 50 micrometer cross section. The method employs Atomic Force Microscope (AFM) or Scanning Tunneling Microscope (STM) acquired surface topologies of deforming specimens to determine (fields of) strains. By way of the method of Digital Image Correlation (DIC), the natural surface roughness features are used as distributed markers. The effect of markers artificially deposited on the surface is examined computationally. Also the significance of other parameters on property measurements, such as surface roughness, has been examined computationally. Initial results obtained using the tensile test apparatus are presented.", "doi": "10.1117/12.324072", "isbn": "9780819429711", "publisher": "Society of Photo-optical Instrumentation Engineers (SPIE)", "place_of_publication": "Bellingham, WA", "publication_date": "1998-09-01", "pages": "66-75" }, { "id": "authors:f0j0s-p8s69", "collection": "authors", "collection_id": "f0j0s-p8s69", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181119-141500977", "type": "book_section", "title": "Round-Robin Tests of Modulus and Strength of Polysilicon", "book_title": "Microelectromechanical Structures for Materials Research", "author": [ { "family_name": "Sharpe", "given_name": "W. N.", "clpid": "Sharpe-W-N" }, { "family_name": "Brown", "given_name": "S.", "clpid": "Brown-S" }, { "family_name": "Johnson", "given_name": "G. C.", "clpid": "Johnson-G-C" }, { "family_name": "Knauss", "given_name": "W.", "clpid": "Knauss-W-G" } ], "contributor": [ { "family_name": "Brown", "given_name": "Stuart", "clpid": "Brown-S" } ], "abstract": "The Young's modulus and strength of polysilicon specimens manufactured in the same production run were measured in four different laboratories. Specimens subjected to in-plane bending were tested at U. C. Berkeley and at Failure Analysis Associates, and tensile measurements were made at Caltech and Johns Hopkins. All specimens were produced at the Microelectronics Center of North Carolina (MCNC). \n\nIn bending, the Young's modulus for specimens nominally 2 \u00b5m thick was measured as 174 GPa and 137 GPa; whereas in tension, a value of 132 GPa was obtained. Modulus values of 136 GPa and 142 GPa were measured in tension on specimens nominally 1.5 \u00b5m and 3.5 \u00b5m thick. Strengths of the brittle polysilicon were 2.8 and 2.7 GPa in bending and 1.3 GPa for both thicknesses in tension.\n\nThese preliminary results were presented at Symposium N - Microelectromechanical Structures for Materials Research at the Materials Research Society meeting in April 1998. This paper is a short overview of the test methods \u2014 each of which is described elsewhere \u2014 and a documentation of the results presented at that time.", "doi": "10.1557/PROC-518-57", "isbn": "9781558994249", "publisher": "Materials Research Society", "place_of_publication": "Warrendale, PA", "publication_date": "1998-04", "pages": "Art. No. 57" }, { "id": "authors:0jnxk-hhn26", "collection": "authors", "collection_id": "0jnxk-hhn26", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200716-135556381", "type": "book_section", "title": "Volume/Shear Interaction in Glassy Polymers", "book_title": "Progress and Trends in Rheology V", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "contributor": [ { "family_name": "Emri", "given_name": "I.", "clpid": "Emri-I" } ], "abstract": "It has been demonstrated in the past that the nonlinear time- or rate-dependent shear behavior of glassy polymers is susceptible to volumetric changes. Following from models based on free volume effects in the glass transition range it has been shown analytically that many effects of nonlinear behavior could possibly be traced to volumetric changes and associated dilatational internal clock mechanisms.", "doi": "10.1007/978-3-642-51062-5_7", "isbn": "978-3-642-51064-9", "publisher": "Springer-Verlag", "place_of_publication": "Heidelberg", "publication_date": "1998", "pages": "21" }, { "id": "authors:bhtq6-m5c35", "collection": "authors", "collection_id": "bhtq6-m5c35", "cite_using_url": "https://resolver.caltech.edu/CaltechGALCITSM:GALCITSM94-5", "type": "monograph", "title": "Deformation Measurements at the Sub-Micron Size Scale: II. Refinements in the Algorithm for Digital Image Correction", "author": [ { "family_name": "Vendroux", "given_name": "G.", "clpid": "Vendroux-G" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "Improvements are proposed in the application of the Digital Image Correlation method, a technique that compares digital images of a specimen surface before and after deformation to deduce its sureface (2-D) displacement field and strains. These refinements, tested on translations and rigid body rotations were significant with regard to the computer efficiency and covergence properties of the method. In addition, the formulation of the algorithm was extended so as to compute the three-dimensional surface displacement field from Scanning Tunneling Microscope tomographies of a deforming specimen. The reolsution of this new displacement measuring method at the namometer scale was assessed on translation and uniaxial tensile tests and was found to be 4.8 nm for in-plane displacement components and 1.5 nm for the out-of-plane one spanning a 10 x 10 \u03bcm area.", "doi": "10.7907/pedw-pd07", "publisher": "California Institute of Technology", "publication_date": "1994-04" }, { "id": "authors:2s6rf-q1x14", "collection": "authors", "collection_id": "2s6rf-q1x14", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:GALCITSM94-5a", "type": "monograph", "title": "Submicron Deformation Field Measurements II: Improved Digital Image Correlation", "author": [ { "family_name": "Vendroux", "given_name": "G.", "clpid": "Vendroux-G" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "This is the second paper in a series of three devoted to the applicaiton of Scanning Tunneling Microscopy to mechanics problems. In this paper improvements to the Digital Image Correlation method are outlined, a technique that compares digital images of a specimen surface before and after deformation to deduce its (2-D) surface displacement field and strains. The necessity of using the framework of large deformation theory for accurately addressing rigid body rotations to reduce associated errors in the strain components is pointed out. In addition, the algorithm is extended to compute the three-dimensional surface displacement field from Scanning Tunneling Microscope data; also, significant improvements are achieved in the rate as well as the robustness of the convergence. For Scanning Tunneling Microscopy topographs the resolution yields 4.8 nm\nfor the in-plane and 1.5 nm for the out-of-plane displacement components spanning an area of 10 \u03bcm x 10 \u03bcm.", "doi": "10.7907/zvy1-mb79", "publisher": "California Institute of Technology", "publication_date": "1994" }, { "id": "authors:xwagk-gen29", "collection": "authors", "collection_id": "xwagk-gen29", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:WAAjam90", "type": "article", "title": "A Mechanical Model for Elastic Fiber Microbuckling", "author": [ { "family_name": "Waas", "given_name": "A. M.", "orcid": "0000-0002-5258-2749", "clpid": "Waas-A-M" }, { "family_name": "Babcock", "given_name": "C. D., Jr.", "clpid": "Babcock-C-D" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "A two-dimensional mechanical model is presented to predict the compressive strength of unidirectional fiber composites using technical beam theory and classical elasticity. First, a single fiber resting on a matrix half-plane is considered. Next, a more elaborate analysis of a uniformly laminated, unidirectional fiber composite half-plane is presented. The model configuration incorporates a free edge which introduces a buckling mode that originates at the free edge and decays into the interior of the half-plane. It is demonstrated that for composites of low volume fraction (<0.3), this decay mode furnishes values of buckling strain that are below the values predicted by the Rosen (1965) model. At a higher volume fraction the buckling mode corresponds to a half wavelength that is in violation of the usual assumptions of beam theory. Causes for deviations of the model prediction from existing experimental results are discussed.", "issn": "0021-8936", "publisher": "Journal of Applied Mechanics", "publication": "Journal of Applied Mechanics", "publication_date": "1990-03-01", "series_number": "1", "volume": "57", "issue": "1", "pages": "138-147" }, { "id": "authors:h3nz9-qgp35", "collection": "authors", "collection_id": "h3nz9-qgp35", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150225-153754137", "type": "article", "title": "A Finite Elastostatic Analysis of Bimaterial Interface Cracks", "author": [ { "family_name": "Ravichandran", "given_name": "G.", "orcid": "0000-0002-2912-0001", "clpid": "Ravichandran-G" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "A numerical method is developed to study the bimaterial interface problem in Neo-Hookean materials under plane stress conditions. Comparison is made with the analytical predictions for the asymptotic field of the problem. The range of dominance of the asymptotic solution at different load levels is established and the amplitudes of the crack-tip asymptotic field are related to the far field loading. The numerical model is extended to analyze the experiments conducted on specimens with an edge crack at the interface between two dissimilar Solithane plates that are characterized by Mooney-Rivlin material behavior.", "doi": "10.1007/BF00047452", "issn": "0376-9429", "publisher": "Springer", "publication": "International Journal of Fracture", "publication_date": "1989-03", "series_number": "1-3", "volume": "39", "issue": "1-3", "pages": "235-253" }, { "id": "authors:r8gpc-ajy15", "collection": "authors", "collection_id": "r8gpc-ajy15", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KNAafr89", "type": "book_section", "title": "Time dependent fracture of polymers", "book_title": "Advances in fracture research : proceedings of the 7th International Conference on Fracture (ICF-7), Houston, Tex., 20-24 March 1989", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "contributor": [ { "family_name": "Salama", "given_name": "K." }, { "family_name": "Ravi-Chandar", "given_name": "K." }, { "family_name": "Taplin", "given_name": "D. M. R." }, { "family_name": "Rama Rao", "given_name": "P." } ], "abstract": "The fracture behavior of polymers is reviewed with emphasis on the time dependent aspects of the problem. Following a delineation of the history of crack propagation investigations in linearly viscoelastic materials, the effects of temperature and solvent environment are examined besides the special effects arising from fatigue loading. These phenomena are examined for both crosslinked and uncrosslinked polymers. Some special consideration is given to the phenomena connected with craze formation in amorphous homopolymers as well as in crystalline materials as exemplified by polyethylene. Finally, status of analytical tools and formulations of fracture problems involving non-linearly viscoelastic material behavior is delineated by means of some examples.", "isbn": "0080343430", "publisher": "Pergamon Press", "place_of_publication": "New York", "publication_date": "1989", "pages": "2683-2711" }, { "id": "authors:tbbzh-t8v82", "collection": "authors", "collection_id": "tbbzh-t8v82", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CHAem83", "type": "article", "title": "Observation of Damage Growth in Compressively Loaded Laminates", "author": [ { "family_name": "Chai", "given_name": "H.", "clpid": "Chai-H" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Babcock", "given_name": "C. D.", "clpid": "Babcock-C-D" } ], "abstract": "An experimental program to determine tie phenomenological aspects of composite-panel failure under simultaneous compressive n-plane loading and low-velocity transverse impact [C-75 m/s (0-250 ft/s)] is described. High-speed photography coupled with the shadow-moir\u00e9 technique is used to record the phenomenon of failure propagation. The information gained from these records, supplemented by plate sectioning and observation for interior damage, has provided information regarding the failure-propagation mechanism.\n\nThe results show that the failure process can be divided roughly into two phases. In the first phase the plane is impacted, and the resulting response causes interlaminar separation. In the second phase the local damage spreads to the undamaged portion of the plate through a combination of laminae buckling and further delamination.", "issn": "0014-4851", "publisher": "Experimental Mechanics", "publication": "Experimental Mechanics", "publication_date": "1983-09-01", "series_number": "3", "volume": "23", "issue": "3", "pages": "329-337" }, { "id": "authors:rzp1g-2dg89", "collection": "authors", "collection_id": "rzp1g-2dg89", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CHAijss81", "type": "article", "title": "One dimensional modelling of failure in laminated plates by delamination buckling", "author": [ { "family_name": "Chai", "given_name": "Herzl", "clpid": "Chai-H" }, { "family_name": "Babcock", "given_name": "Charles D.", "clpid": "Babcock-C-D" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "abstract": "When low speed objects impact composite laminated plates delamination may result. Under inplane compression such delaminations may buckle and tend to enlarge the delaminated area which can lead to loss of global plate stability.\n\nThis process is modelled here in a first attempt by a delaminating beam-column wherein the local delamination growth, stability and arrest are governed by a fracture mechanics-based energy release rate criterion.", "doi": "10.1016/0020-7683(81)90014-7", "issn": "0020-7683", "publisher": "Elsevier", "publication": "International Journal of Solids and Structures", "publication_date": "1981-11", "series_number": "11", "volume": "17", "issue": "11", "pages": "1069-1083" }, { "id": "authors:ty2ms-93n89", "collection": "authors", "collection_id": "ty2ms-93n89", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KNAjap80", "type": "article", "title": "On the hygrothermomechanical characterization of polyvinyl acetate", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Kenner", "given_name": "V. H.", "clpid": "Kenner-V-H" } ], "abstract": "As a part of a program to understand the mechanisms of failure in time-dependent adhesion and film bonding, the creep compliance of polyvinyl acetate (PVAc) in shear has been determined both as a function of temperature and absorbed moisture. Volumetric expansion as a function of temperature or moisture takeup was also measured. We find that practically realizable changes in moisture content affect both the creep compliance and the swelling of PVAc to a degree comparable to that resulting from realistic changes in temperature. For example, the creep rates (histories) at corresponding times for PVAc subjected to 92% relative humidity storage are accelerated by approximately four orders of magnitude over those found for the dry material. Moreover, we find within reasonable experimental error that water concentration affects the time scale of creep like temperature through a concentration-dependent shift factor. An attempt is made at discussing the interrelation of temperature- and moisture-induced volume changes.", "doi": "10.1063/1.327458", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1980-10-01", "series_number": "10", "volume": "51", "issue": "10", "pages": "5131-5136" }, { "id": "authors:g0z1h-3et95", "collection": "authors", "collection_id": "g0z1h-3et95", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:GalcitSM80-18", "type": "publication_deliverable", "title": "Final Report to the Air Force Office of Scientific Research on Hygroviscoelasticity of the Human Intervertebral Disc", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "In order to gain an improved understanding of the behavior of human intervertebral disc material under various kinds of loads the viscoelastic properties of small specimens excised from human L4-L5 discs were examined. Excisions were made from donated spine segments procured a few hours after death and then frozen. Material examined was in the form of single lamellar specimens as well as specimens containing several lamellae. \n\nTensile relaxation tests were performed on single lamellae prepared such that the collagen fibers were a) aligned with the tension axis, b) normal to the tension axis and c) at an angle of about 30[degrees] with that axis. The multi-lamellar specimens were excised from the disc such that one set produced the tensile axis to run parallel to the disc circumference (surrounding the spinal axis) while another set caused the tensile axis to run parallel to the spinal axis. \n\nIt was found early in the study that the water content of the disc material has a profound effect on its mechanical response. Consequently the diffusion and swelling characteristics of the material in different water environments were studied. Primarily air of differing relative humidity and various concentrated solutions of NaCl were used to provide for different water concentrations in the material. \n\nFor the relaxation studies the same environments were used. This allowed achieving water concentrations ranging from virtually dry to in-vivo conditions. \n\nThe main findings of this work are: \n\n1) Water affects the relaxation time in a sensitive way. A few percent change in water content can change the relaxation time by an order of magnitude or more. This fact is important when one is concerned with laboratory testing without being able to control the water content at all times. \n\n2) Diffusion is a surprisingly slow process taking place over several hours (2-3) in specimens only 1/2 mm thick. The\namount of water take-up is controlled by the environment (distilled water destroys samples into fissures) and by constraints offered by the fiber structure and the stresses it engenders (see point 5) below). \n\n3) The stiffness of the disc material is on the order of 3 to 10 x 10^-6 N/m^2; relaxation occuring, on the whole rather slowly, i.e., on the order of 10% per decade. The relaxation modulus at right angles to the collagen fibers is about 1/3 that of the modulus along the fiber direction. \n\n4) The relaxation modulus of multi-layer specimens cut from the disc in a circumferential and a spine-axial direction are very nearly the same; the modulus for the circumferential material is slightly higher. The consequence of this would be that although one would expect a markedly anisotropic behavior of the disc material on the basis of its fiber and lamellar construction, the disc material does not deviate very strongly from isotropic response. (Isotropy as-referred to a plane that is tangent to the disc perimetric surface.) \n\n5) Stress affects the equilibrium concentration of water in the material. The implication - and test result - is that once the stress has changed the equilibrium of water content with the environment is disturbed and the concentration changes. That change, in turn, causes a change in relaxation behavior such that tensile stresses cause an acceleration of relaxation or creep (softening), while compression would cause the opposite affect (hardening). The material responds thus to stress as a system that is open to the environment.", "publisher": "California Institute of Technology", "publication_date": "1980-07-01" }, { "id": "authors:4vxp2-b1x37", "collection": "authors", "collection_id": "4vxp2-b1x37", "cite_using_url": "https://resolver.caltech.edu/CaltechGALCITSM:GALCITSM80-18", "type": "monograph", "title": "Hygroviscoelasticity of the Human Intervertebral Disc: Final Report", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "In order to gain an improved understanding of the behavior of human intervertebral disc material under various kinds of loads the viscoelastic properties of small specimens excised from human L4-L5 discs were examined. Excisions were made from donated spine segments procured a few hours after death and then frozen. Material examined was in the form of single lamellar specimens as well as specimens containing several lamellae. \n\nTensile relaxation tests were performed on single lamellae prepared such that the collagen fibers were a) aligned with the tension axis, b) normal to the tension axis and c) at an angle of about 30[degrees] with that axis. The multi-lamellar specimens were excised from the disc such that one set produced the tensile axis to run parallel to the disc circumference (surrounding the spinal axis) while another set caused the tensile axis to run parallel to the spinal axis. \n\nIt was found early in the study that the water content of the disc material has a profound effect on its mechanical response. Consequently the diffusion and swelling characteristics of the material in different water environments were studied. Primarily air of differing relative humidity and various concentrated solutions of NaCl were used to provide for different water concentrations in the material. \n\nFor the relaxation studies the same environments were used. This allowed achieving water concentrations ranging from virtually dry to in-vivo conditions. \n\nThe main findings of this work are: \n\n1) Water affects the relaxation time in a sensitive way. A few percent change in water content can change the relaxation time by an order of magnitude or more. This fact is important when one is concerned with laboratory testing without being able to control the water content at all times. \n\n2) Diffusion is a surprisingly slow process taking place over several hours (2-3) in specimens only 1/2 mm thick. The\namount of water take-up is controlled by the environment (distilled water destroys samples into fissures) and by constraints offered by the fiber structure and the stresses it engenders (see point 5) below). \n\n3) The stiffness of the disc material is on the order of 3 to 10 x 10^-6 N/m^2; relaxation occuring, on the whole rather slowly, i.e., on the order of 10% per decade. The relaxation modulus at right angles to the collagen fibers is about 1/3 that of the modulus along the fiber direction. \n\n4) The relaxation modulus of multi-layer specimens cut from the disc in a circumferential and a spine-axial direction are very nearly the same; the modulus for the circumferential material is slightly higher. The consequence of this would be that although one would expect a markedly anisotropic behavior of the disc material on the basis of its fiber and lamellar construction, the disc material does not deviate very strongly from isotropic response. (Isotropy as-referred to a plane that is tangent to the disc perimetric surface.) \n\n5) Stress affects the equilibrium concentration of water in the material. The implication - and test result - is that once the stress has changed the equilibrium of water content with the environment is disturbed and the concentration changes. That change, in turn, causes a change in relaxation behavior such that tensile stresses cause an acceleration of relaxation or creep (softening), while compression would cause the opposite affect (hardening). The material responds thus to stress as a system that is open to the environment.", "doi": "10.7907/qx6y-c525", "publisher": "California Institute of Technology", "publication_date": "1980-07" }, { "id": "authors:6p33b-x9e56", "collection": "authors", "collection_id": "6p33b-x9e56", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141114-131259517", "type": "monograph", "title": "The Incorporation of Bending into the Buckling Delamination Analysis: Informal Progress Report No. 3", "author": [ { "family_name": "Chai", "given_name": "H.", "clpid": "Chai-H" }, { "family_name": "Babcock", "given_name": "C. D.", "clpid": "Babcock-C-D" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "In a previous report a one dimensional model of buckling-delamination in a column was summarized. The main assumption made in that report was that the unbuckled portions of the column can be assumed to remain straight. The purpose of this report is to investigate the\nmore general problem in which bending effects are taken into account. We deal here with the case of a single off center delamination in a column. (The case of multi-delaminations in a column can be worked out too\nunder slight modifications.) Following the general procedure outlined in previous reports, consider the column of unit width shown in fig, la, State I represents the unstressed column while state I1 denotes the\naxially and uniformally compressed column. State III differs from II by allowing the delamination to buckle. Our aim here is to find an\nexpression for the strain energy release rate of state III.", "doi": "10.7907/jvgn-3580", "publisher": "California Institute of Technology", "publication_date": "1979-11" }, { "id": "authors:3c3ef-57s65", "collection": "authors", "collection_id": "3c3ef-57s65", "cite_using_url": "https://resolver.caltech.edu/CaltechGALCITSM:GALCITSM77afosr77-3139", "type": "monograph", "title": "Viscoelastic Behavior of the Human Intervertebral Disc Under Consideration of Moisture Migration", "author": [ { "family_name": "Panagiotacopulos", "given_name": "N. D.", "clpid": "Panagiotacopulos-N-D" }, { "family_name": "Bloch", "given_name": "R.", "clpid": "Bloch-R" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Harvey", "given_name": "P.", "clpid": "Harvey-P" }, { "family_name": "Patzakis", "given_name": "M.", "clpid": "Patzakis-M" } ], "abstract": "The human intervertebral disc is a highly inhomogeneous fiber composite pressure vessel. If damaged in the post-infant stage, the disc does not repair and may need surgical correction. Diagnosis of whether a disc is damaged is difficult at best and, at this time, involves invasive techniques which are not free of danger (injection of x-ray opaque liquids). Starting from a desire to develop a noninvasive diagnostic technique based on x-ray and computer aided image enhancement, we became interested in the mechanical properties of the disc. These would be important in gaging the x-ray detected deformations of the disc under various loads. During the course of this work we became aware of another need of diagnostics related to estimating the proclivity of an intact disc to sustain damage under unusual loads. It turns out that the water content of the disc material dominates its mechanical behavior. Since modern medical equipment such as the EMI-x-ray body-scanner may record quantitatively the water content of the internal body organs, the possibility exists to gage in-vivo water content measurements with the mechanical performance of discs. \n\nBecause the layers of the disc's annulus fibrosous are so thin, we have had difficulty in preparing single-layer specimens. So far, we have worked mainly with three-layer specimens. That test geometry has been sufficient to establish several important aspects of the mechanical properties. \n\nWe find that the relaxation behavior is very sensitive to moisture content. Accordingly we have worked with carefully controlled environments including saline solutions claimed to represent body conditions. A major difficulty in obtaining repeatable results is obtaining straight test specimens and holding them in the clamps of the testing apparatus. If moisture and temperature conditioning was repeated without reclamping the specimen, reasonably repeatable results were obtained. No aging was observed after repeated drying and moisturizing cycles. \n\nWe also found that water diffuses slowly in the layers. The water apparently acts similar to the solvent in a polymer, effecting a change in the relaxation times. Increasing water content causes shortening of relaxation times, drying having the opposite effect. Upon controlling the water content of the specimen we are thus able to measure the relaxation behavior in various time domains. Data covering a wide spectrum of relaxation times is presented which includes all of the time scales experienced by the human body. This mechanical characterization gives us an estimate of how discs respond to different rates of deformation and loading conditions. \n\nIt is of interest to note that with age (past age 30) the moisture content of the human disc decreases (possible other changes involving increased cross-link density of the mucopolysaccharides as well as an exchange of mucopolysaccharides for collagen). As a result one would expect the human intervertebral disc to react more stiffly with increasing age under nearly constant speeds of motion. Combining this observation with the changes in the vigor of motion/muscle activity as a function of age allows a tentative explanation of the statistic that the largest incidence of disc problems occur around age 40-50.", "doi": "10.7907/ynhb-7j56", "publisher": "California Institute of Technology", "publication_date": "1977-06-27" }, { "id": "authors:tz9hp-22r78", "collection": "authors", "collection_id": "tz9hp-22r78", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:MUEtsr71", "type": "article", "title": "The Fracture Energy and Some Mechanical Properties of a Polyurethane Elastomer", "author": [ { "family_name": "Mueller", "given_name": "H. K.", "clpid": "Mueller-H-K" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "The energy required to form a unit of new surface in the fracture of a polyurethane elastomer is determined. The rate sensitivity of the material has been reduced by swelling it in toluene. This paper primarily describes the experimental work of measuring the lower limit of the fracture energy. With this value and the creep compliance as a basis, the rate dependence of fracture energy for the unswollen material has been determined. It is thus shown that the dependence of the fracture energy on the rate of crack propagation can be explained by energy dissipation around the tip of the crack. Good agreement between the theoretically and experimentally determined relationships for the rate-sensitive fracture energy is demonstrated.", "doi": "10.1122/1.549209", "issn": "0038-0032", "publisher": "Transactions of the Society of Rheology", "publication": "Transactions of the Society of Rheology", "publication_date": "1971-07-01", "series_number": "2", "volume": "15", "issue": "2", "pages": "217-233" }, { "id": "authors:3gt1w-5fq78", "collection": "authors", "collection_id": "3gt1w-5fq78", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141223-103711656", "type": "article", "title": "Crack propagation in a linearly viscoelastic strip", "author": [ { "family_name": "Mueller", "given_name": "H. K.", "clpid": "Mueller-H-K" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "The tip velocity of a crack propagating through a viscoelastic material depends on geometry, applied load and its history, and material properties. A consideration of the work done by the unloading tractions at the crack tip shows that, for a large crack propagating through an infinitely long strip under constant lateral strain, the rate of propagation can be calculated from a knowledge of the intrinsic fracture energy (a material constant), the material creep compliance, and an additional size parameter. This parameter vanishes from the analysis if the material is elastic, and the familiar instability criterion is obtained in this case. Comparison with experimental data is provided and the consequences of step loadings are examined.", "doi": "10.1115/1.3408801", "issn": "0021-8936", "publisher": "American Society Mechanical Engineers", "publication": "Journal of Applied Mechanics", "publication_date": "1971-06", "series_number": "2", "volume": "38", "issue": "2", "pages": "483-488" }, { "id": "authors:99j7b-6wc70", "collection": "authors", "collection_id": "99j7b-6wc70", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150319-145121332", "type": "article", "title": "Delayed Failure - The Griffith Problem for Linearly Viscoelastic Materials", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "The unstable growth of a crack in a large viscoelastic plate is considered, within the framework of continuum mechanics. Starting from the local stress and deformation fields at the tip of the crack, a non-linear, first order differential equation is found to describe the time history of the crack size if the stress applied far from the crack is constant. The differential equation contains the creep compliance and the intrinsic surface energy of the material. The surface energy concept for viscoelastic materials is clarified. Inertial effects are not considered, but the influence of temperature is included for thermorheologically simple materials. \n\nInitial crack velocities are given as a function of applied load in closed form, as well as a comparison of calculated crack growth history with experiments. Above a certain high stress, crack propagation ensues at high speeds controlled by material inertia while at a lower limit infinite time is required to produce crack growth. Thus an upper and lower limit criterion of the Griffith type exists. For rate insensitive (elastic) materials the two limits coalesce and only the brittle fracture criterion of Griffith exists. The implications of these results for creep fracture in metals and inorganic glasses are examined.", "doi": "10.1007/BF00183655", "issn": "0376-9429", "publisher": "Wolters-Noordhoff Publishing", "publication": "International Journal of Fracture", "publication_date": "1970-03", "series_number": "1", "volume": "6", "issue": "1", "pages": "7-20" }, { "id": "authors:zchsn-0aw63", "collection": "authors", "collection_id": "zchsn-0aw63", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KNAtsr69", "type": "article", "title": "Stable and Unstable Crack Growth in Viscoelastic Media", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "The failure of load-bearing structures by fracture is generally important in all phases of our society. It may concern small household items as well as expensive structures of civil or space applications and accordingly may cause varying degrees of economic distress. While the state of failure is usually easily determined as either \"not failed\" or \"completely failed,\" the estimation of how close to either state a structure is, poses a much more difficult problem. It is important to recognize, however, that from an engineering point of view, the latter problem is the important one because it would allow, in principle, the prediction of the conditions leading to fracture and thus to a close estimate of the service life of a structure. \n\nInasmuch as failures by fracture involve the growth of cracks it appears that keeping track of the size of a crack in a particular structure provides a means of assessing *quantitatively* the strength prior to complete failure. If one agrees that the description of structural strength is rationalized in terms of the size of the defects, it foll0ws that one must attempt to understand the laws that govern the growth of such defects in order to predict complete failure. \n\nFracture of materials is a complicated process which encompasses atomistic aspects, as well as microscopic and large-scale continuum mechanical considerations. Although one of these aspects should not be considered without the other we shall be concerned with the continuum-mechanical formulation of the problem of fracture growth in viscoelastic materials. From this viewpoint the prediction of failure comprises three phases: first an examination of the physical situation presented by a static or growing defect in a material, second the translation of this physically observable situation into a mathematical model which is amenable to analysis by currently available or extendable tools of mathematics, third the theoretical exploitation of the mathematical model in an attempt to predict the behavior of defects under load and the comparison of these results with experimentally observable phenomena to assess the validity of the modelling process as given from phase one and phase two. \n\nWhile there are many important details that have bearing on such a development we shall be concerned more with the principles of the analysis and show how the various considerations of the three phases enter into the overall structure of the crack propagation problem. In keeping analytic work as simple as possible it is intended to emphasize what type of results may be obtained with the aid of continuum mechanics and where continuum mechanics requires support by microscopic considerations.", "doi": "10.1122/1.549134", "issn": "0038-0032", "publisher": "Transactions of the Society of Rheology", "publication": "Transactions of the Society of Rheology", "publication_date": "1969-09-01", "series_number": "3", "volume": "13", "issue": "3", "pages": "291-313" }, { "id": "authors:qt436-saw79", "collection": "authors", "collection_id": "qt436-saw79", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CLAtsr68", "type": "article", "title": "On the Numerical Determination of Relaxation and Retardation Spectra for Linearly Viscoelastic Materials", "author": [ { "family_name": "Clauser", "given_name": "John F.", "clpid": "Clauser-J-F" }, { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "abstract": "Knowledge of the relaxation spectrum is important because (1) it provides an intrinsic characterization of the mechanical properties for linearly viscoelastic materials and (2) it offers a rational way to derive the coefficients for a Prony or Dirichlet series representation of the relaxation modulus of importance to some engineering analyses. A numerical solution based on Simpson quadrature leads to an unstable solution in the sense that a decrease in integration intervals produces a progressively worse solution which oscillates between positive and negative values. This difficulty may be overcome by requiring that the curvature of the relaxation spectrum with respect to the relaxation times be minimized. The method is tested on the modified power law and good agreement with the exact and numerically determined relaxation spectrum is obtained. However, when the same method is used to determine the retardation spectrum, only the unstable solution is obtained, although the form of the integral equation is the same. This different behavior is attributed to the difference in the characteristics of the relaxation and retardation spectral functions.", "doi": "10.1122/1.549103", "issn": "0038-0032", "publisher": "Transactions of the Society of Rheology", "publication": "Transactions of the Society of Rheology", "publication_date": "1968-01-01", "series_number": "1", "volume": "12", "issue": "1", "pages": "143-153" }, { "id": "authors:a2z2w-q7y23", "collection": "authors", "collection_id": "a2z2w-q7y23", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151125-113158676", "type": "book_section", "title": "Fatigue Failure in Linearly Viscoelastic Masterials", "author": [ { "family_name": "Williams", "given_name": "M. L.", "clpid": "Williams-M-L" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Wagner", "given_name": "F. R.", "clpid": "Wagner-F-R" } ], "abstract": "The thermodynamic approach to the fracture of linearly viscoelastic materials presented earlier is extended to include fatigue. The theoretical analysis of the growth of an internal spherical flaw due to a uniformly distributed,\noscillatory input of displacement in the radial direction predicts a growth-rest type of flaw growth which depends upon the properties of the media and the loading frequency. Comparison of these results with experimental\ncrack growth data for a pre-cracked sheet specimen subjected to an oscillatory displacement input discloses a qualitative similarity in behavior. It is, therefore, believed that the analytical model employed is representative of real flaw behavior and that its study can reveal the main features of macroscopic flaw-growth.", "publisher": "Chemical Propulsion Information Agency", "publication_date": "1966" }, { "id": "authors:35ez5-7fe83", "collection": "authors", "collection_id": "35ez5-7fe83", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151125-113438967", "type": "book_section", "title": "Time-Dependent Failure of Viscoelastic Materials Under Cyclic Loads", "author": [ { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" } ], "abstract": "The problem of failure in viscoelastic materials under cyclic strain histories is treated theoretically by using a fracture model based on the theory of rate processes. Failure times in constant, uniaxial strain tests are compared with failure times encountered\nin sinusoidal strain histories. The dependence of the latter on the mean strain, the size of the strain variation and its frequency is illustrated. It is pointed out that for certain conditions a difference in the failure times in constant or cyclic strain histories may be\nmasked entirely by statistical data scatter. Finally the failure of solid propellant fuels under cyclic loading is discussed in the light of the results derived for a continuum rubber.", "publisher": "Chemical Propulsion Information Agency", "publication_date": "1966" }, { "id": "authors:2g0fj-g2k30", "collection": "authors", "collection_id": "2g0fj-g2k30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100519-091001010", "type": "book_section", "title": "On the mechanical properties of an H-C rubber", "author": [ { "family_name": "Knauss", "given_name": "Wolfgang G.", "clpid": "Knauss-W-G" } ], "abstract": "The material properties of H-C binder including dynamic shear compliance, relaxation modulus, creep compliance, ultimate stress and ultimate strain are reported. Further useful information in the form of Modified Power Law and Prony Series curve fits are included as well as a master curve of reduced stress vs. strain. \n\nAll tests are performed using standard procedures; however some inconsistency in material properties has been found. It was further determined that the time-temperature shift principle is not directly applicable in its simplest form; however, upon postulating two molecular mechanisms responsible for gross deformations it is found that each one can be associated with a different characteristic glass transition temperature such that, e.g. the dynamic compliance J(w) is the sum of two compliances J_\u03b1 and J_\u03b3 \n\nJ(w,t) = J_\u03b1(w, T^\u03b1_glass) + J_\u03b3(w, T^\u03b3_glass) \n\nwhich individually follow the time temperature superposition principle.", "publisher": "Caltech Library", "publication_date": "1963-11" }, { "id": "authors:5dasw-zyj96", "collection": "authors", "collection_id": "5dasw-zyj96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150604-135847602", "type": "monograph", "title": "Fundamental Studies Relating to Systems Analysis of Solid Propellants, January 1, 1960-May 31, 1960", "author": [ { "family_name": "Blatz", "given_name": "P. J.", "clpid": "Blatz-P-J" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Schapery", "given_name": "R. A.", "clpid": "Schapery-R-A" }, { "family_name": "Williams", "given_name": "M. L.", "clpid": "Williams-M-L" } ], "abstract": "Previous reports of this series have attempted to\ndefine some of the important parameters affecting structural\nintegrity of solid propellant rocket grains. Three general\nareas have been discussed, namely material properties,\nanalytical procedures, and criteria for mechanical failure.\n\nThis particular report is devoted to failure criteria,\nincluding both limiting deformation and fracture. First of all, the characteristic material properties of filled and unfilled elastomers are described, followed by a brief description of current and proposed tests which can be conducted to obtain experimental information relating to these characteristics in such a form that they can be incorporated in structural integrity analyses. In particular, the necessity for multi-axial\ntests is stressed in conjunction with minor requirements\nfor new experimental equipment.\n\nThe selection of appropriate fracture criteria is discussed.\nMost progress, however, can be reported only in criteria for\nunfilled elastomers for small and large strains where it appears a distortion strain energy density may be used. It is necessary to delay any really definitive remarks upon filled elastomers or actual grain composites, and subsequent use with cumulative\ndamage analyses, until additional experimental data for propellants is forthcoming.", "doi": "10.7907/6wsw-zw77", "publisher": "California Institute of Technology", "publication_date": "1960-06-15" }, { "id": "authors:ge1wj-66q37", "collection": "authors", "collection_id": "ge1wj-66q37", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151203-165233805", "type": "monograph", "title": "Fundamental Studies Relating to Systems Analysis of Solid Propellants, October l, 1959-December 31, 1959", "author": [ { "family_name": "Blatz", "given_name": "P. J.", "clpid": "Blatz-P-J" }, { "family_name": "Knauss", "given_name": "W. G.", "clpid": "Knauss-W-G" }, { "family_name": "Schapery", "given_name": "R. A.", "clpid": "Schapery-R-A" }, { "family_name": "Stimpson", "given_name": "L. D.", "clpid": "Stimpson-L-D" }, { "family_name": "Williams", "given_name": "M. L.", "clpid": "Williams-M-L" } ], "abstract": "Previous reports of this series have attempted to define some of the important parameters affecting the structural integrity of solid propellant rocket grains. Three general areas have been discussed, namely material properties, analytical procedures, and criteria for mechanical\nfailure.\n\nThis particular report is devoted to a more detailed examination of the properties of a filled viscoelastic resin, and their representation by appropriate mechanical models. In addition, a comparison of two methods of computing viscoelastic strains in a pressurized cylinder is\npresented.\n\nIn the category of material properties, linear viscoelastic model theory is reviewed, and certain important relations among sets of experimental data are deduced. A justification for the application of this theory is provided by the analytic representation of available dynamic\ndata in terms of a well-known distribution function. Since the inception of this work additional experimental data on propellants has become available.\n\nIn the category of analytical procedures, the usual approach of representing material properties by a four-element model, as determined from the dynamic data in a limited frequency range, is compared with the\nmore sophisticated Fourier transform method in which the entire frequency range is utilized. The two approaches are applied to calculate the viscoelastic hoop strain at the inner boundary of an internally pressurized infinitely\nlong hollow cylinder subjected to a ramp-type pressure pulse. In this example, the dilatation is assumed elastic or frequency independent and the distortion viscoelastic.\n\nIn the following quarter, primary effort will be devoted to the determination of a criterion for mechanical failure of propellants. Two steps are involved. One is the analytical representation of ultimate strain as a function of temperature on strain rate by means of a mechanical model. In addition to the usual distribution of relaxation (or retardation) times, this model will be supplied with a distribution of ultimate strain. Step two involves\nthe choice of a suitable criterion for compounding ultimate strain or ultimate stress components into a single parameter, which, when exceeded at a given\nrate and temperature, denotes the onset of fracture or mechanical failure.", "doi": "10.7907/0sxn-1k84", "publisher": "California Institute of Technology", "publication_date": "1960-01-15" } ]