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

A theory of crack initiation and growth in viscoelastic media

Soft materials are materials with a low shear modulus relative to their bulk modulus and where elastic restoring forces are mainly of entropic origin. A sparse population of strong bonds connects molecules together and prevents macroscopic flow. In this review we discuss the current state of the art on how these soft materials break and detach from solid surfaces. We focus on how stresses and strains are localized near the fracture plane and how elastic energy can flow from the bulk of the material to the crack tip. Adhesion of pressure-sensitive-adhesives, fracture of gels and rubbers are specifically addressed and the key concepts are pointed out. We define the important length scales in the problem and in particular the elasto-adhesive length Γ/E where Γ is the fracture energy and E is the elastic modulus, and how the ratio between sample size and Γ/E controls the fracture mechanisms. Theoretical concepts bridging solid mechanics and polymer physics are rationalized and illustrated by micromechanical experiments and mechanisms of fracture are described in detail. Open questions and emerging concepts are discussed at the end of the review.

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Fracture and adhesion of soft materials: a review.

The theory of crack growth developed in Parts I and II is used to predict crack velocity and failure time for an elastomer under simple uniaxial and biaxial stress states. Included are consideration of the effect of specimen size on failure time for initially small cracks, experimental determination of fracture properties, the effect of strain level on crack propagation, and the validity of the plane strain assumption. The second half of the paper examines the effect upon crack velocity of nonlinear viscoelasticity of failing material at the crack tip in media which is otherwise linearly viscoelastic. The dependence of fracture behavior on environmental changes and aging is also considered.RésuméOn utilise la théorie de croissance de la fissure développée dans les parties I et II pour réduire la vitesse de fissuration et le temps de rupture d'un élastomére soumis à des états de contraintes uniaxiales et biaxiales. Le mémoire comporte des considérations sur l'effet de la dimension des éprouvettes sur le temps de rupture au départ de petites fissures, la détermination expérimentale des propriétés de la rupture, l'étude de l'effet du niveau de déformation sur la propagation des fissures, et de la validité d'hypothèses d'état plan de déformation.La seconde partie de l'article comporte l'examen de l'effet d'une viscoélasticité non linéaire dans la matière qui se rompt à la pointe d'une fissure, laquelle est par ailleurs sise dans un milieu caractérisé par une viscoélasticité linéaire.On considère également la manière dont le comportement à la rupture dépend du vieillissement et des changements de l'environnement.

A theory of crack initiation and growth in viscoelastic media: III. Analysis of continuous growth

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.

Competing fracture in kinetically controlled transfer printing.

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.

A theory of crack initiation and growth in viscoelastic media II. Approximate methods of analysis

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

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H. K. Mueller

Papers

Crack Propagation in a Linearly Viscoelastic Strip