Yueguang Wei

STEADY-STATE CRACK GROWTH AND WORK OF FRACTURE FOR SOLIDS CHARACTERIZED BY STRAIN GRADIENT PLASTICITY

Mode I steady-state crack growth is analysed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by a generalization of JZ flow theory which accounts for the influence of the gradients of plastic strains on hardening. The constitutive model involves one new parameter, a material length 1, specifying the scale of nonuniform deformation at which hardening elevation owing to strain gradients becomes important. Gradients of plastic strain at a sharp crack tip result in a substantial increase in tractions ahead of the tip. This has important consequences for crack growth in materials that fail by decohesion or cleavage at the atomic scale. The new constitutive law is used in conjunction with a model which represents the fracture process by an embedded traction-separation relation applied on the plane ahead of the crack tip. The ratio of the macroscopic work of fracture to the work of the fracture process is calculated as a function of the parameters characterizing the fracture process and the solid, with particular emphasis on the role of 1. 0 1997 Elsevier Science Ltd

Interface strength, work of adhesion and plasticity in the peel test

A cohesive zone model is proposed and analyzed for steady-state peeling of a thin rate-independent, elastic-plastic film bonded to an elastic substrate. A traction-separation description of the interface is embedded within continuum characterizations of the film and substrate. The primary parameters characterizing the traction-separation relation are the work of adhesion and the peak separation stress, termed the interface strength. The objective of the study is the determination of the relationship of the peel force to the work of adhesion of the interface and its strength, with due regard for plastic deformation in the film. An example of an elastic film peeled from an elastic-plastic substrate is also presented.

Interface adhesion: effects of plasticity and segregation

Abstract The adhesion at interfaces between dissimilar materials is strongly affected by both segregation and the extent of plasticity in the adjoining material, particularly when one of these is a metal (or thermoplastic). It will be shown that these interfaces when clean, are generally strong and tough, such that failure occurs in one of the adjoining materials, rather than at the interface. However, segregrants and contaminants often embrittle and weaken the interface, especially in combination with ambient moisture. The embrittlement is obviated either by alloying with elements that “getter” the contaminants or by using an “adhesion layer” that has essentially the same effect: Cr and Ti are particularly effective gettering elements. Models that relate these effects to fundamental material parameters through non-dimensional indices are described. They comprise linkages between atomistic and continuum, enabled by implementation of a plasticity length scale, within the context of a crack growth simulation routine. Comparison with the experimental results is conducted, leading to suggestions for development of a predictive scheme.

Models of Interface Separation Accompanied by Plastic Dissipation at Multiple Scales

Two continuum mechanical models of interface fracture for interfaces joining materials where at least one undergoes plastic deformation are reviewed and examined critically. The embedded process zone model (EPZ model) has an adhesive zone, characterized by a work of separation and an interface strength, embedded within a continuum model of the adjoining materials. The SSV model imposes an elastic, plasticity-free layer of prescribed thickness between the interface and the surrounding elastic-plastic continuum. Crack advance requires the work of separation to be supplied by the local elastic crack tip field. The objective of each model is to provide the relation between the macroscopic interface toughness (the total work of fracture) and the work of separation. Under steady-state crack growth, the total work of fracture is the work of separation plus the work of plastic dissipation, the latter often far exceeding the former. It will be argued that each model has its own domain of validity, subject to the accuracy of conventional continuum plasticity at small scales, but neither is able to capture the dramatic trends which have been observed in macroscopic toughness measurements stemming from alterations in interface bonding conditions. A unified model is proposed which coincides with the two models in their respective domains of validity and provides a transition between them. Interface separation energy and interface strength (the peak separation stress) each play a central role in the unified model. Strain gradient plasticity is used to illustrate the effect of plastic deformation at the micron scale on the link between interface and macroscopic properties.

Nonlinear delamination mechanics for thin films

Delamination of prestressed thin films on thick substrates is analysed accounting for plastic dissipation in either the substrate or film. Emphasis is on large scale yielding wherein the height of the plastic zone at the propagating interface crack tip is comparable to the film thickness. Such conditions are common for both metal and polymer thin films on elastic substrates or for ceramic coatings on metal substrates when the interface between the film and substrate is reasonably strong. Under large scale yielding, the notion of a thickness-independent interface toughness no longer pertains, and a nonlinear fracture mechanics is required to quantify delamination. Two such approaches are pursued in this paper using models based on the attainment of critical conditions at the interface crack tip within the plastic zone. Steady-state film delamination is analysed for conditions where yielding occurs either in the film or in the substrate, and critical combinations of prestress and thickness are predicted. The theory is applied to a recent set of experiments on copper films delaminating from silica substrates.

Edge cracks in plastically deforming surface grains

A selection of surface crack problems is presented to provide insights into Stage I and early Stage II fatigue crack growth. Edge cracks at 45 o and 90 o to the surface are considered for cracks growing in single crystals. Both single crystal slip and conventional plasticity are employed as constitutive models. Edge cracks at 45 o to the surface are considered that either (i) kink in the direction perpendicular to the surface, or (ii) approach a grain boundary across which only elastic deformations occur.  2001 Editions scientifiques et medicales Elsevier SAS

Size-dependent elastic modulus and vibration frequency of nanocrystals

The elastic properties and the vibration characterization are important for the stability of materials and devices, especially for nanomaterials with potential and broad application. Nanomaterials show different properties from the corresponding bulk materials; the valid theoretical model about the size effect of the elastic modulus and the vibration frequency is significant to guide the application of nanomaterials. In this paper, a unified analytical model about the size-dependent elastic modulus and vibration frequency of nanocrystalline metals, ceramics and semiconductors is established based on the inherent lattice strain and the binding energy change of nanocrystals compared with the bulk crystals, and the intrinsic correlation between the elasticity and the vibration properties is discussed. The theoretical predictions for Cu, Ag, Si thin films, nanoparticles, and TiO2 nanoparticles agree with the experimental results, the computational simulations, and the other theoretical models.

Thin layer splitting along the elastic-plastic solid surface

Thin layer splitting along the elastic-plastic solid surface is studied based on the elastic-plastic fracture mechanics method. In the splitting process, since the split arm does not undergo the reversed plastic bending, comparing with the conventional peel test method, the split test has remarkable advantages in measuring the material fracture behavior and is recommended as a new test method. Moreover, besides the driving force parameter, the split test method provides an additional measurable parameter, a residual curvature (or curvature radius) of the split arm. Comparing with the peeling force, the split force also has the connection with the total energy release rate, which is related with the crack tip separation energy (or material fracture toughness), separation strength, and the plastic dissipation work. Through measuring the driving force and the residual curvature, the fracture toughness and separation strength can be obtained. The primary objective of the present research is to develop a series of relations of the split force, the residual curvature, as well as the crack tip slope angle, respectively with the split layer thickness and material parameters, when crack tip advances steadily. Frictionless (or smooth) contact between splitter head and split arm surface is assumed. Another objective of the present research is to explore a connection between the split test solutions and the peel test solutions. Finally, the split test analysis is applied to a wedge-loaded double-cantilever beam experiment for Al-alloy material, a considerably similar test method with the split test, conducted by Thouless and his collaborators, and the fracture parameters from both test systems are correlated.

Mixed Mode Interface Toughness Of Metal / Ceramic Joints

A mechanics study of the interface toughness of joints comprised of ceramic substrates joined by a thin ductile metal layer is carried out for arbitrary combinations of mode I and mode II loading. The crack lies on one of the metal/ceramic interfaces, and the mechanism of separation at the crack tip is assumed to be atomic decohesion. The SSV model proposed by Suo, Shih and Varias is invoked. This model employs a very narrow elastic strip imposed between the substrate and the ductile layer to model the expected higher hardness of material subject to high strain gradients and possible dislocation-free zone in the immediate vicinity of the crack tip. The criterion for crack advance is the requirement that energy release rate at the crack tip in this narrow elastic strip be the atomistic work of fracture. The contribution of plastic dissipation in the metal layer to the total work of fracture is computed as a function of the thickness and yield strength of the layer and of the relative amount of mode II to mode I. Ductile joints display exceptionally strong thickness and mixed mode dependencies.

Overall mechanical behavior of nanocrystalline materials accompanied by damage evolution on grain boundaries

In the present research, overall mechanical behaviors of the nanocrystalline materials considering the grain boundary damage evolutions are investigated systematically. A mixed-mode cohesive interface model is used to describe the mixed deformation and fracture process of grain boundaries. Based on the mixed-mode cohesive interface model, the grain boundary damage and damage evolution are defined and characterized. In order to describe the size effect, the strain gradient plasticity theory is used for grain materials. In the present results, the overall stress–strain relations and the corresponding damage evolution curves are obtained as functions of several independent parameters, such as the mixed separation strength, the mixed critical energy release rate, grain size, Young’s modulus as well as strain hardening exponent. The present results show that both the overall strength and ductility of the nanocrystalline materials are closely dependent on the grain boundary strength and the damage evolution behaviors. By means of the damage evolution relations, the features of the overall stress–strain curves can be clearly interpreted.