Methods of quasi-static deformation and fracture analysis are developed for a class of nonlinear viscoelastic media and sample applications are given. Selection of the class of media is guided by actual rheological behavior of monolithic and composite materials as well as the need for simplicity to be able to understand the effect of primary material and continuum parameters on crack growth behavior. First, pertinent aspects of J integral and energy release rate theory for nonlinear elastic media are discussed. Nonlinear viscoelastic constitutive equations are then given, and correspondence principles which establish a simple relationship between mechanical states of elastic and viscoelastic media are developed. These principles provide the basis for the subsequent extension of J integral theory to crack growth in viscoelastic materials. Emphasis is on predicting mechanical work available at the crack tip for initiation and continuation of growth; some examples show how viscoelastic properties and the J integral affect growth behavior. Included is the problem of a crack in a thin layer having different viscoelastic properties than the surrounding continuum. The Appendix gives an apparently new constitutive theory for elastic and viscoelastic materials with changing microstructure (e.g. distributed damage) and indicates the conditions under which the fracture theory in the body of the paper is applicable.

Correspondence principles and a generalized J integral for large deformation and fracture analysis of viscoelastic media

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 contact behavior of solid materials is determined by the system geometry, externally applied loads and internal adhesive forces, and by the materials properties. As the size and stiffness of a material decrease, adhesive forces become increasingly important in determining its contact behavior. The current trends toward the use of smaller features in many areas of technology, and the importance of ‘soft’ materials including biological tissues, elastomers and polymer gels, demand that the effects of adhesion on contact mechanics be properly understood. The focus of this review is on the mechanics of contact experiments that are commonly used to characterize adhesion, and on the materials science of adhesion of elastic and viscoelastic materials.

Contact mechanics and the adhesion of soft solids

Reversible control of adhesion is an important feature of many desired, existing, and potential systems, including climbing robots, medical tapes, and stamps for transfer printing. We present experimental and theoretical studies of pressure modulated adhesion between flat, stiff objects and elastomeric surfaces with sharp features of surface relief in optimized geometries. Here, the strength of nonspecific adhesion can be switched by more than three orders of magnitude, from strong to weak, in a reversible fashion. Implementing these concepts in advanced stamps for transfer printing enables versatile modes for deterministic assembly of solid materials in micro/nanostructured forms. Demonstrations in printed two- and three-dimensional collections of silicon platelets and membranes illustrate some capabilities. An unusual type of transistor that incorporates a printed gate electrode, an air gap dielectric, and an aligned array of single walled carbon nanotubes provides a device example.

https://www.pnas.org/content/pnas/107/40/17095.full.pdf

Microstructured elastomeric surfaces with reversible adhesion and examples of their use in deterministic assembly by 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 mechanics of quasi-static crack closing and bonding of surfaces of the same or different linear viscoelastic materials is described. Included is a study of time-dependent joining of initially curved surfaces under the action of surface forces of attraction and external loading. Emphasis is on the use of continuum mechanics to develop equations for predicting crack length or contact size as a function of time for relatively general geometries; atomic and molecular processes associated with the healing or bonding process are taken into account using a crack tip idealization which is similar to that used in the Barenblatt method for fracture. Starting with a previously developed correspondence principle, an expression is derived for the rate of movement of the edge of the bonded area. The effects of material time-dependence and the stress intensity factor are quite different from those for crack growth. A comparison of intrinsic and apparent energies of fracture and bonding is made, and criteria are given for determining whether or not bonding can occur. Examples are given to illustrate use of the basic theory for predicting healing of cracks and growth of contact area of initially curved surfaces. Finally, the effect of bonding time on joint strength is estimated from the examples on contact area growth.

On the mechanics of crack closing and bonding in linear viscoelastic media

Equations are developed for predicting crack growth in the opening mode for quite general situations, including many quasi-static and dynamic problems involving moisture and temperature gradients in monolithic and composite materials. Except for the small zone of failing material at the crack tip, the body is assumed to be linearly viscoelastic. A method for obtaining viscoelastic stresses and displacements from elastic solutions is first described. The traction boundary condition for the crack faces is not in general satisfied by these results. However, it is shown by modifying the failure zone in the elastic problem this condition can be met, and an integral equation for the stress in the modified failure zone is derived. Approximate analysis similar to that used previously by the author in stress analysis is then employed to solve the integral equation and develop relatively simple equations for predicting crack speed; these equations relate crack speed in the viscoelastic material to stress intensity factors in a suitably defined elastic body.

R. A. Schapery

Papers

Correspondence principles and a generalized J integral for large deformation and fracture analysis of viscoelastic media

A theory of crack initiation and growth in viscoelastic media

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

On the mechanics of crack closing and bonding in linear viscoelastic media

A method for predicting crack growth in nonhomogeneous viscoelastic media