Effective elastic modulus of bone-like hierarchical materials

A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is compared with that based on the tension-shear chain model and finite element simulation, respectively. It is shown that all three models can be used to describe the mechanical behavior of the hierarchical material when the number of hierarchy levels is small. By increasing the number of hierarchy level, the shear-lag result is consistent with the finite element result. However the tension-shear chain model leads to an opposite trend. The transition point position depends on the fraction of hard phase, aspect ratio and modulus ratio of hard phase to soft phase. Further discussion is performed on the flaw tolerance size and strength of hierarchical materials based on the shear-lag analysis

Microstructure Observation And Mechanical Behavior Modeling For Limnetic Nacre

In the present research, microstructure of a kind of limnetic shell (Hyriopsis cumingii) is observed and measured by using the scanning electron microscopy, and mechanical behavior experiments of the shell nacre are carried out by using bending and tensile tests. The dependence of mechanical properties of the shell nacre on its microstructure is analyzed by using a modified shear-lag model, and the overall stress-strain relation is obtained. The experimental results reveal that the mechanical properties of shell nacre strongly depend on the water contents of the limnetic shell. Dry nacre shows a brittle behavior, whereas wetting nacre displays a strong ductility. Compared to the tensile test, the bending test overestimates the strength and underestimates the Young's modulus. The modified shear-lag model can characterize the deformation features of nacre effectively

Particulate Size Effects in the Particle-Reinforced Metal-Matrix Composites

The influences of I,article size on the mechanical properties of the particulate metal matrix composite;are obviously displayed in the experimental observations. However, the phenomenon can not be predicted directly using the conventional elastic-plastic theory. It is because that no length scale parameters are involved in the conventional theory. In the present research, using the strain gradient plasticity theory, a systematic research of the particle size effect in the particulate metal matrix composite is carried out. The roles of many composite factors, such as: the particle size, the Young's modulus of the particle, the particle aspect ratio and volume fraction, as well as the plastic strain hardening exponent of the matrix material, are studied in detail. In order to obtain a general understanding for the composite behavior, two kinds of particle shapes, ellipsoid and cylinder, are considered to check the strength dependence of the smooth or non-smooth particle surface. Finally, the prediction results will be applied to the several experiments about the ceramic particle-reinforced metal-matrix composites. The material length scale parameter is predicted

A New Finite Element Method for Strain Gradient Theories and Applications to Fracture Analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J2 deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip

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

A Multiscale Model for the Ductile Fracture of Crystalline Materials

In this paper, a multiscale model that combines both macroscopic and microscopic analyses is presented for describing the ductile fracture process of crystalline materials. In the macroscopic fracture analysis, the recently developed strain gradient plasticity theory is used to describe the fracture toughness, the shielding effects of plastic deformation on the crack growth, and the crack tip field through the use of an elastic core model. The crack tip field resulting from the macroscopic analysis using the strain gradient plasticity theory displayes the 1/2 singularity of stress within the strain gradient dominated region. In the microscopic fracture analysis, the discrete dislocation theory is used to describe the shielding effects of discrete dislocations on the crack growth. The result of the macroscopic analysis near the crack tip, i.e. a new K-field, is taken as the boundary condition for the microscopic fracture analysis. The equilibrium locations of the discrete dislocations around the crack and the shielding effects of the discrete dislocations on the crack growth at the microscale are calculated. The macroscopic fracture analysis and the microscopic fracture analysis are connected based on the elastic core model. Through a comparison of the shielding effects from plastic deformation and the discrete dislocations, the elastic core size is determined

Peeling Experiments Of Ductile Thin Films Along Ceramic Substrates - Critical Assessment Of Analytical Models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al2O3 substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al2O3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al2O3 substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case. (C) 2007 Elsevier Ltd. All rights reserved

Measurements and simulations of interface behavior in metal thin film peeling along ceramic substrate

Peeling experiments for aluminum thin film along the Al2O3 substrate are carried out, and the variations of external driving force (energy release rate) at the steady-state delamination of the thin film in the metal film/ceramic substrate system are measured. Additionally, theoretical modeling for the thin film delamination is also performed. Based on the bending model, three double-parameter criteria are used. Three double-parameter criteria include: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the interfacial crack tip slope angle of thin film, and (3) the interfacial fracture toughness and the critical von Mises effective strain of thin film-at crack tip. Based on the three double-parameter criteria, the thin film nonlinear peeling problems are solved analytically for each case. The results show that the solutions of thin film nonlinear peeling based on the bending model are very sensitive to the model parameter selections. Through analyses and comparisons to different solutions, a connection between solutions based on the bending models and based on the two-dimensional elastic-plastic finite element analysis is obtained. The effective regions of each model can be specified through comparing the present experimental result with model solutions

Failure mechanism researches of material surface and interface in micro-scratch test

In the present research, the adhesion properties and failure mechanisms for a ductile thin film on a silicon substrate (Ni/Si) are studied experimentally, and are simulated theoretically. In the experimental research, the relations of the horizontal driving force, vertical displacement and the frictional coefficients with horizontal displacement are measured. Furthermore, the variation of the total energy release rate and the frictional coefficient between contact surfaces are measured through obtaining a frictional effect law. The law displays that the frictional influences on the energy release rate of the total system weakly depend on the thin film thickness. This conclusion leads to that the frictional effect can be eliminated in the toughness ratio relation approximately. So that one can directly obtain the interfacial adhesion toughness from measurements in the micro-scratching test. In addition, the micro-scratching process for the ductile thin film/brittle substrate systems is simulated using the double cohesive zone model. Prediction results of the energy release rate are obtained, and are compared with the experimental results obtained in the present research

Solutions and discussions of thin film undergoing the nonlinear peeling

Based on the bending model, three double-parameter criteria characterizing thin film peeling process are introduced and analyzed in detail. Three double-parameter criteria include: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the interfacial crack tip slope angle of thin film, and (3) the interfacial fracture toughness and the critical von Mises effective strain of thin film at crack tip. Based on the three double-parameter criteria, the thin film nonlinear peeling problems are solved analytically for each case. The results show that the solutions of thin film nonlinear peeling based on the bending model are very sensitive to the model parameter selections. Through analyses and comparisons for different solutions, a connection between solutions based on the bending models and based on the two-dimensional elastic-plastic finite element analysis is obtained