N. Aravas

Elastoplastic analysis of the peel test

Abstract A theoretical analysis of the peeling of a thin elastoplastic film bonded on an elastic substrate is presented in this paper. The moment-curvature relation for pure bending of an elastoplastic beam under conditions of plane strain is derived and slender beam theory is used to analyze the deformation of the adherend. Large deformation finite element analysis is used to study in detail the stress and deformation fields in the area near the tip of the interfacial crack. An analysis of steady slate peeling and a method for the calculation of the work expenditure during steady state peeling are presented. An energy balance is used to relate an experimentally measured peel force to the specific fracture energy.

Hydrogen induced shear localization of the plastic flow in metals and alloys

Hydrogen enhanced localized plasticity (HELP) is a viable mechanism for hydrogen embrittlement supported by experimental observations. According to the HELP mechanism, hydrogen induced premature failures result from hydrogen induced plastic instability which leads to hydrogen assisted localized ductile processes. The objective of this work is to reveal the role of hydrogen in possibly localizing the macroscopic deformation into bands of intense shear using solid mechanics methodology. The hydrogen effect on material deformation is modeled through the hydrogen induced volume dilatation and the reduction in the local flow stress upon hydrogen dissolution into the lattice. Hydrogen in assumed to reside in both normal interstitial lattice sites (NILS) and reversible traps associated with the plastic deformation. The analysis of the plastic deformation and the conditions for plastic flow localization are carried out in plane strain uniaxial tension. For a given initial hydrogen concentration in the unstressed specimen, a critical macroscopic strain is identified at which shear localization commences.

DETERMINATION OF HIGHER-ORDER TERMS IN ASYMPTOTIC ELASTOPLASTIC CRACK TIP SOLUTIONS

A METHODOLOGY for the calculation of higher-order terms in asymptotic elastoplastic crack tip solutions is developed. The J2-deformation plasticity theory with power law hardening is used to describe the constitutive behavior of the continuum. A two-term expansion of the solution in the near crack tip region is developed. Plane stress and plane strain solutions for a crack in a homogeneous material as well as for a crack lying along the interface between a rigid substrate and an elastoplastic medium are obtained. For the case of a plane strain crack in a homogeneous material, it is shown that, when the hardening capacity of the material is small, the effects of elasticity enter the asymptotic solution to third order or higher, when there is substantial hardening, however, elastic effects enter the solution to second order and the magnitude of the second term in the expansion of the solution is controlled by the J-integral. THE CHARACTERIZATION of the stress and deformation fields in the region near the tip of a crack is essential for the development of sound fracture criteria. HUTCHINSON (1968) and RICE and ROSENGREN (1968) developed the elastoplastic asymptotic solution for the near-tip stresses in a homogeneous material (known as the HRR solution) and showed that the magnitude of the dominant term in the expansion of the solution is determined by the J-integral (RICE, 1968). If the region of dominance of the leading-order term in the expansion of the solution is sufficiently larger than the region over which the fracture micro-mechanisms take place, then the J-integral can be used as the fracture parameter. If the region of J-dominance, however, is smaller than the fracture process zone, then two or more parameters may enter the fracture criterion. LI and WANG 0986) suggested the use of a parameter k2, which is the magnitude of the second term in the near-tip stress plastic solution, as the second parameter to be used together with the J-integral in the fracture criterion. BETEGrN and HANCOCK (1991) used a modified boundary layer formulation of the small-scale yielding problem, in which the boundary conditions are defined in terms of the mode I stress intensity factor Kt and the constant stress term T that enters the near-tip expansion of the elastic solution (LARSSON and CARLSSON, 1973; RICE, 1974), and

Mixed finite element formulations of strain-gradient elasticity problems

Theories on intrinsic or material length scales find applications in the modeling of size-dependent phenomena. In elasticity, length scales enter the constitutive equations through the elastic strain energy function, which, in this case, depends not only on the strain tensor but also on gradients of the rotation and strain tensors. In the present paper, the strain-gradient elasticity theories developed by Mindlin and co-workers in the 1960s are treated in detail. In such theories, when the problem is formulated in terms of displacements, the governing partial differential equation is of fourth order. If traditional finite elements are used for the numerical solution of such problems, then C 1 displacement continuity is required. An alternative ‘‘mixed’’ finite element formulation is developed, in which both the displacement and the displacement gradients are used as independent unknowns and their relationship is enforced in an‘‘integralsense’’. A variational formulation is developed which can be used for both linear and non-linear strain-gradient elasticity theories. The resulting finite elements require only C 0 continuity and are simple to formulate. The proposed technique is applied to a number of problems and comparisons with available exact solutions are made. � 2002 Elsevier Science B.V. All rights reserved.

FINITE ELEMENT ANALYSIS OF VOID GROWTH NEAR A BLUNTING CRACK TIP

Abstract Large deformation finite element analysis has been used to study the near crack tip growth of long cylindrical holes aligned parallel to the plane of a mode I plane strain crack. The near crack tip stress and deformation fields are analyzed. The results show that the holes are pulled towards the crack tip and change their shape to approximately elliptical with the major axis radial to the crack. They also grow faster directly ahead of the crack than at an angle to the crack plane. Several crack-hole coalescence criteria are discussed and estimates for the conditions for fracture initiation are given and compared with experimental results. The range of estimates now available from finite element calculations coincides quite well with the range of experimental data for materials containing inclusions which are only loosely bonded to the matrix.

On the effect of hydrogen on plastic instabilities in metals

Experimental observations and theoretical calculations have demonstrated that hydrogen solute atoms increase the dislocation mobility in metals and alloys, thus promoting highly localized plastic processes which eventually lead to localized ductile rupture. While the underlying mechanism for hydrogen-enhanced dislocation mobility is well understood, little is known on how this mechanism acting at the microscale can lead to macroscopic plastic instability. In this paper, a theoretical investigation is carried out in a specimen under plane-strain tension in an effort to understand how hydrogen-induced softening and lattice dilatation at the microscale can lead to macroscopic i) shear localization (shear banding bifurcation) or ii) necking bifurcation.  2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

The analysis of void growth that leads to central bursts during extrusion

USING large deformation finite element analysis together with Gurson’s constitutive model, we have studied the behavior of microvoids nucleated at second phase particles during direct axisymmetric extrusion. Two different die-designs were analyzed. Experiments show that the first die-design results in central burst formation while the second gives a solid product free of central bursts. Comparison of the stress fields of the two die-designs provides a possible explanation of how central bursting initiates and why it appears after several steps of multi-step extrusions. The finite element results are in agreement with experimental observation and show that the finite element method can be successfully used to predict the formation of central bursts during extrusion.

Finite element implementation of gradient plasticity models Part I: Gradient-dependent yield functions

Abstract Theories with intrinsic or material length scales find applications in the modeling of size-dependent phenomena such as, for example, the localization of plastic flow into shear bands. In gradient-type plasticity theories, length scales are introduced through the coefficients of spatial gradients of one or more internal variables. The present work undertakes the variational formulation and finite element implementation of two families of gradient-type plasticity models in which higher-order gradients of the state variables enter the yield function (in Part I) or the evolution equations for the state variables (in Part II). As an example, the application to a gradient-type version of the von Mises plasticity model is described in detail in the present paper. Numerical examples of localization under plane strain tension are considered using both the gradient-type (non-local) model, and its corresponding classical (local) counterpart. An important consequence of using the non-local model is that the numerical solution does not exhibit the pathological mesh-dependence that is evident when the standard von Mises model is used.

Finite element implementation of gradient plasticity models. Part II : Gradient-dependent evolution equations

Abstract The variational formulation, and finite element implementation of a class of plasticity models with gradient-dependent yield functions is covered in detail in Part I. In this sequel, attention is focussed upon the finite element formulation, and implementation of a different class of plasticity models wherein spatial gradients of one or more internal variables enter the evolution equations for the state variables. Finite element solutions are obtained for the problems of localization of plastic flow in plane strain tension, and of a mode-I plane strain crack. The pathological dependence of the finite element solution on the size of the elements in local plasticity models disappears when the gradient-type model is used.

On the mechanics of adhesion testing of flexible films

Abstract The peel test is a simple mechanical test used by microelectronics industries to measure the adhesion of thin films bonded on dielectric substrates. When the film deforms elastically during peeling, the peel force is a direct measure of the adhesive fracture energy. However, when inelastic deformation takes place, the interpretation of the experimental data is not as straightforward. A general formulation of the problem of peeling is given and solutions for metallic and polymeric films are presented. The results of the analysis reveal the effects of several parameters of the peel test, such as the mechanical properties and the thickness of the film, and provide a systematic way for the determination of the adhesive fracture energy from an experimentally measured peel force.