Delayed failure - The Griffith problem for linearly viscoelastic materials
01 Mar 1970-International Journal of Fracture (Wolters-Noordhoff Publishing)-Vol. 6, Iss: 1, pp 7-20
TL;DR: In this paper, the unstable growth of a crack in a large viscoelastic plate is considered, within the framework of continuum mechanics, and 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.
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.
Initial 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.
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TL;DR: In this paper, a theory is developed for predicting the time-dependent size and shape of cracks in linearly viscoelastic, isotropic media, and a local energy criterion of failure at the tip is introduced, which is applicable to both constant and transient tip velocities.
Abstract: A theory is developed for predicting the time-dependent size and shape of cracks in linearly viscoelastic, isotropic media First, the effect of a narrow zone of disintegrating material at the crack tip on opening displacement and on a finite stress distribution ahead of the tip is examined for elastic materials Extension to viscoelastic media is then made Although the undamaged portion of the continuum is assumed linear, no significant restrictions are placed on the nature of the zone of failing material at the crack tip and, therefore, this material may be highly nonlinear, rate-dependent, and even discontinuous Finally, formulation of the problem is completed by introducing a local energy criterion of failure at the tip which is applicable to both constant and transient tip velocities Parts II–IV, to appear in succeeding issues, will cover approximate methods of analysis and several applications of the theory
566 citations
Abstract: This article attempts to review the progress achieved in the understanding of scaling and size ef fect in the failure of structures. Particular emphasis is placed on quasi brittle materials for which the size etTect is important and complicated. After reflections on the long history of size effect studies, attention is focused on three main types of size effects, namely the statistical size effect due to randomness of strength, the energy release size effect, and the possible size effect due to fractality of fracture or microcracks. Definitive conclusions on the applicability of these theories are drawn. Subsequently, the article discusses the application of the known size effect law for the measurement of material fracture properties, and the modeling of the size effect by the cohesive crack model, non local finite element models and discrete element models. Extensions to com pression failure and to the rate-dependent material behavior are also outlined. The damage con stitutive law needed for describing a microcracked material in the fracture process zone is dis cussed. Various applications to quasibrittle materials, including concrete, sea ice, fiber compos ites, rocks and ceramics are presented. There are 377 references included in this article.
318 citations
TL;DR: Temperature plays an important role in kinetically controlled transfer printing with its influences, making it advantageous to pickup printable objects at the reduced temperatures and to print them at the elevated ones.
Abstract: Transfer printing by kinetically switchable adhesion to an elastomeric stamp shows promise as a powerful micromanufacturing method to pickup microstructures and microdevices from the donor substrate and to print them to the receiving substrate. This can be viewed as the competing fracture of two interfaces. This paper examines the mechanics of competing fracture in a model transfer printing system composed of three laminates: an elastic substrate, an elastic thin film, and a viscoelastic member (stamp). As the system is peeled apart, either the interface between the substrate and thin film fails or the interface between the thin film and the stamp fails. The speed-dependent nature of the film/stamp interface leads to the prediction of a critical separation velocity above which separation occurs between the film and the substrate (i.e., pickup) and below which separation occurs between the film and the stamp (i.e., printing). Experiments verify this prediction using films of gold adhered to glass, and the theoretical treatment extends to consider the competing fracture as it applies to discrete micro-objects. Temperature plays an important role in kinetically controlled transfer printing with its influences, making it advantageous to pickup printable objects at the reduced temperatures and to print them at the elevated ones.
281 citations
TL;DR: In this paper, simple approximate relations are derived for predicting the time of fracture initiation and crack tip tip velocity in linearly viscoelastic media, assuming that the second derivative of the logarithm of creep compliance is small.
Abstract: Starting with equations developed in Part I for the opening mode of displacement, simple, approximate relations are derived for predicting the time of fracture initiation and crack tip velocity in linearly viscoelastic media. First we use the assumption that the second derivative of the logarithm of creep compliance with respect to logarithm of time is small (which is normally valid for viscoelastic materials); we next derive a relation between instantaneous values of tip velocity and stress intensity factor. This result is then used to examine some characteristics of crack growth behavior. Finally, some results are obtained for the separate problem of predicting the time at which propagation initiates.
252 citations
TL;DR: In this paper, a general compliance formulation of the cohesive crack model was proposed for concrete structures, where the fracture process zone (cohesive zone) is large and cannot be neglected in comparison to the structure dimensions.
Abstract: The time dependence of fracture has two sources: (1) the viscoelasticity of material behavior in the bulk of the structure, and (2) the rate process of the breakage of bonds in the fracture process zone which causes the softening law for the crack opening to be rate-dependent. The objective of this study is to clarify the differences between these two influences and their role in the size effect on the nominal strength of stucture. Previously developed theories of time-dependent cohesive crack growth in a viscoelastic material with or without aging are extended to a general compliance formulation of the cohesive crack model applicable to structures such as concrete structures, in which the fracture process zone (cohesive zone) is large, i.e., cannot be neglected in comparison to the structure dimensions. To deal with a large process zone interacting with the structure boundaries, a boundary integral formulation of the cohesive crack model in terms of the compliance functions for loads applied anywhere on the crack surfaces is introduced. Since an unopened cohesive crack (crack of zero width) transmits stresses and is equivalent to no crack at all, it is assumed that at the outset there exists such a crack, extending along the entire future crack path (which must be known). Thus it is unnecessary to deal mathematically with a moving crack tip, which keeps the formulation simple because the compliance functions for the surface points of such an imagined preexisting unopened crack do not change as the actual front of the opened part of the cohesive crack advances. First the compliance formulation of the cohesive crack model is generalized for aging viscoelastic material behavior, using the elastic-viscoelastic analogy (correspondence principle). The formulation is then enriched by a rate-dependent softening law based on the activation energy theory for the rate process of bond ruptures on the atomic level, which was recently proposed and validated for concrete but is also applicable to polymers, rocks and ceramics, and can be applied to ice if the nonlinear creep of ice is approximated by linear viscoelasticity. Some implications for the characteristic length, scaling and size effect are also discussed. The problems of numerical algorithm, size effect, roles of the different sources of time dependence and rate effect, and experimental verification are left for a subsequent companion paper.
154 citations
Cites background from "Delayed failure - The Griffith prob..."
...Knauss (1970; 1989; 1993) considered the crack opening displacement to be determined by the (nonaging) viscoelastic properties of the bulk material, and the crack resistance to be represented by the normal traction (cohesive stress)....
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...…velocity growth of an infinitely long crack in an infinite body made of standard viscoelastic material. frac4167.tex; 2/12/1997; 11:57; v.7; p.2 Knauss (1970; 1989; 1993) considered the crack opening displacement to be determined by the (nonaging) viscoelastic properties of the bulk material,…...
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References
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6,510 citations
4,028 citations
TL;DR: The resistance to tearing of a rubber vulcanizate is usually determined by loading in a specified manner a test-piece of the vulcanizer of standard shape, in which a notch has been produced, either in the molding process or by cutting the testpiece in a standard fashion.
Abstract: The resistance to tearing of a rubber vulcanizate is usually determined by loading in a specified manner a test-piece of the vulcanizate of standard shape, in which a notch has been produced, either in the molding process or by cutting the test-piece in a standard fashion. A wide variety of shapes of test-piece and notch and of methods of loading have been recommended by various authors (see, for example, Buist1).
1,142 citations
"Delayed failure - The Griffith prob..." refers background in this paper
...The surface energy F.After Rivlin and Thomas [ 26 ] suggested the energy concept for the fracture of rubber, Thomas [27] demonstrated that the energy required to propagate a crack depended on the speed of propagation....
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