International Journal of Damage Mechanics recent issues

Professor T.H. Lin Memorial Issue in The International Journal of Damage Mechanics

Sun, L., Ju, J. W. — 2008-07-07

PQR Model-based Micromechanical Analysis of Hysteresis Loops for Single Crystal Fatigue: Aspects of Multi-Axial Loading, Geometric Effects and Creep

Dongdong Wang, , Tung Hua Lin, — 2008-07-07

The micromechanical theory of fatigue crack initiation, namely the PQR model with a gating mechanism proposed by Lin (1992), is systematically summarized and further generalized to arbitrary loading conditions which may occur in reality. All possible loading cases and slip mechanisms are considered for a FCC single crystal. The Schmid factors for both primary and secondary slip systems are presented. A 3D boundary element method is adopted to compute the stress influence coefficients for the residual stress field. The hysteresis loops, which are due to a general two phase sequential loading process, i.e., a uni-axial loading followed by a multi-axial loading applied by combined shear and axial loadings, are given to illustrate the fatigue development and demonstrate the proposed methodology. The results show that the two stage loading may increase the magnitudes of intrusion and extrusion. Subsequently the geometry influence for intrusion is studied. The effect of geometry variation caused by intrusion is taken into account through updating the stress influence coefficients as well as the applied resolved stress when intrusion grows. This process is continued until the saturated state of fatigue crack initiation is reached. Comparison of geometry influence on intrusion growth is shown as well. It turns out that the geometric change could become an important factor for the intrusion growth. Finally by replacing the plastic strain with creep strain the present model is easily extended to investigate the steady hysteresis loops for single crystal creep at elevated temperature. The results compare favorably with the available experimental data.

Micromechanical Elastoplastic Damage Modeling of Progressive Interfacial Arc Debonding for Fiber Reinforced Composites

Ju, J.W., Ko, Y.F. — 2008-07-07

This study presents a new micromechanical elastoplastic progressive damage model to predict the effective transverse mechanical behavior and interfacial arc microcrack evolution of fiber-reinforced composites. The partial debonding process at the fiber—matrix interfaces is represented by the growing debonding angles of arc microcracks. Progressive partially debonded cylindrical isotropic fibers are replaced by equivalent orthotropic yet perfectly bonded elastic cylindrical fibers. The equivalent orthotropic elastic moduli are constructed to characterize the reduction of the load-transfer capacity in the debonded directions. The effective elastic moduli of four-phase composites are derived by using a micromechanical formulation. In order to characterize the overall transverse elastoplastic damage behavior, an effective yield criterion is derived on the basis of the ensemble-area averaging procedure and the first-order effects of eigenstrains upon yielding. The proposed effective yield criterion, coupling with the overall plastic flow rule and the hardening law, comprises the analytical framework for the prediction of effective elastoplastic-damage responses of ductile matrix composites containing randomly located yet aligned cylindrical fibers. The Weibull's probabilistic function is utilized to characterize the varying probability of progressive interfacial arc microcracks, governed by the internal stresses of fibers and the interfacial bonding strength. The proposed micromechanical elastoplastic-damage model is then applied to the transverse uniaxial and transverse biaxial tensile loading with varied stress ratios. Comparisons between the present predictions and available experimental data, as well as other numerical simulations, are performed to elucidate the potential of the proposed formulation.

A Note on Short-time Response of Two-dimensional Lattices during Dynamic Loading

Mastilovic, S. — 2008-07-07

The disordered 2D lattices are used extensively to study damage evolution and fracture of inhomogeneous or multi-phase systems. The present note addresses their initial elastic response during dynamic loading. Namely, a transition from short-time values of modulus of elasticity and Poisson's ratio to respective long-time values, which is not accompanied by the corresponding change of stiffness tensor components. The study is performed on three 2D truss-type lattices. It is demonstrated that the difference between the two sets of elastic properties is a result of combining effects of the initial lateral inertia and the disorder of the system.

Flexure Toughness of Polymer Fiber-reinforced Cementitious Materials

Punyamurtula, V. K., Yu Qiao, — 2008-07-07

In this article, the toughening effect of polymer fibers in cementitious materials is analyzed through an energy method. When a crack front encounters a fiber array, additional fracture work is required to overcome the barrier effect. The influences of fibers, matrix, and crack length on the critical energy release rate are collectively described by a single system parameter.

Professor T.H. Lin Memorial Issue in The International Journal of Damage Mechanics

Lizhi Sun, , Ju, J.-W. W. — 2008-05-16

In Memoriam of Professor T.H. Lin: A Giant and The Kindest Gentleman

Ju, J. W. — 2008-05-16

Study of the Damage-induced Anisotropy of Quasi-brittle Materials using the Component Assembling Model

Jing Zhang, , Liang, N.-G., Deng, S.-C., Liu, J.-X., Liu, X.-Y., Qiang Fu, — 2008-05-16

Damage-induced anisotropy of quasi-brittle materials is investigated using component assembling model in this study. Damage-induced anisotropy is one significant character of quasi-brittle materials coupled with nonlinearity and strain softening. Formulation of such complicated phenomena is a difficult problem till now. The present model is based on the component assembling concept, where constitutive equations of materials are formed by means of assembling two kinds of components' response functions. These two kinds of components, orientational and volumetric ones, are abstracted based on pair-functional potentials and the Cauchy—Born rule. Moreover, macroscopic damage of quasi-brittle materials can be reflected by stiffness changing of orientational components, which represent grouped atomic bonds along discrete directions. Simultaneously, anisotropic characters are captured by the naturally directional property of the orientational component. Initial damage surface in the axial-shear stress space is calculated and analyzed. Furthermore, the anisotropic quasi-brittle damage behaviors of concrete under uniaxial, proportional, and nonproportional combined loading are analyzed to elucidate the utility and limitations of the present damage model. The numerical results show good agreement with the experimental data and predicted results of the classical anisotropic damage models.

Investigation of the Crack-Dislocation Interaction Effects

Ju, J.W., Sejin Oh, — 2008-05-16

The objective of the current work is to investigate the interaction effects between a crack and an array of dislocations under various configurations using the elasticity theory. By treating the crack and dislocations as singularities in the elastic field of a material, we examine their collective stress and displacement responses near the crack tip at the micromechanical level. First, the stationary formulation for a crack interacting with a single dislocation is presented, and the effects of dislocation upon the crack tip field are systematically assessed under different spatial configurations. This stress—displacement analysis shows that the crack remains open at all times for the blunting dislocations, while the crack closure is observed at the tip for wake dislocations. Subsequently, the elastic theory of crack-multiple dislocations interaction is rigorously studied by considering three types of forces exerted on the dislocations along different slip planes. Specifically, the slip forces exerted on a typical dislocation are due to the influences from the external loading, its own image dislocations, and other interacting dislocations as well as all their image dislocations. Furthermore, the dislocation emission criterion defined by Lin and Thomson is employed, and the behavior of multiple dislocations is systematically investigated. Finally, the effective stress intensity factor, the shielding of the crack tip from the dislocation array, the geometric dislocation distributions, and the dislocation-free zone are explored in detail.

Anisotropic Elastoplastic and Damage Behavior of SiCp/Al Composite Sheets

Skolnik, D.A., Liu, H.T., Wu, H.C., Sun, L.Z. — 2008-05-16

A combined experimental and modeling research is performed to study the anisotropic elastoplastic and damage responses of SiC particle-reinforced Al composite sheets. To investigate the effects of the composite processing, two sets of specimens cut from the heat-treated and as-rolled composite sheets are tested under uniaxial loading. The dependence of the strength, plastic flow, and strain ratios on the rolling angles are discussed in detail. To model the phenomena observed in the experiments, a micromechanics-based damage framework is further developed. The interfacial debonding and the rolling angle's effects are integrated into this model. Good consistency between the experimental results and the analytical predications demonstrates the validity of the theoretical model.

Effective Stress and Vector-valued Orientational Distribution Functions

Yang, Q., Chen, X., Zhou, W.-Y. — 2008-03-12

The original Kachanov—Rabotnov damage variable is inherently microplane-based and should be expressed by a scalar-valued orientation distribution function (ODF), and the corresponding effective stress is a vector-valued ODF. The analysis of vector-valued ODFs is established in this article in the spirit of the analysis of scalar-valued ODFs by Kanatani, K. (1984a). Distribution of Directional Data and Fabric Tensors, International Journal of Engineering Science, 22: 149—164 and Kanatani, K. (1984b). Stereological Determination of Structural Anisotropy, International Journal of Engineering Science, 22: 531—546. Explicit expansions of vector-valued ODFs up to the sixth-order have been developed, and the relationship of fabric tensors of different order is addressed. The fabric tensors and expansion of the Kachanov—Rabotnov effective stress vector can be fully determined by the scalar-valued ODF characterizing the microplane damage. The second-order effective stress and damage tensors of Murakami, S. (1988). Mechanical Modeling of Material Damage, ASME Journal of Engineering Materials and Technology, 55: 280—286 are related to the second-order expansion of the Kachanov—Rabotnov effective stress vector. Therefore, the analysis of vector-valued ODFs furnishes a rigorous and unified mathematical basis for the damage theory of Kachanov, L.M. (1958). Time of the Rupture Process under Creep Conditions, Izv. Akad. Nauk., USSR. Otd. Tekhn. Nauk. 8: 26—31, Rabotnov, I.N. (1963). On the Equations of State for Creep, Progress in Applied Mechanics, the Prager Anniversary, 8: 307—315, and Murakami, S. (1988). Mechanical Modeling of Material Damage, ASME Journal of Engineering Materials and Technology, 55: 280—286.

Influence of Interfacial Bond Strength on Fatigue Life and Thermo-Mechanical Behavior of a Particulate Composite: An Experimental Study

Basaran, C., Nie, S., Hutchins, C.S., Ergun, H. — 2008-03-12

Experimental studies conducted on a particular cast acrylic composite demonstrate the significant influence of the interfacial bond strength between filler particles and the polymer matrix on the fatigue life, and mechanical properties. The composite studied in this project is composed of a ductile matrix, which is lightly cross-linked poly-methyl methacrylate (PMMA) and hard, brittle alumina trihydrate (ATH) agglomerate particle filler. In the study, high, moderate, and low levels of interfacial adhesion between the matrix and the filler are investigated, while all the other material properties are kept constant. Monotonic tension and fatigue tests are conducted at different temperatures. Material degradation is presented in terms of elastic modulus degradation, load-drop parameter, and plastic strain range.

Modeling of the Degradation of Elastic Properties due to the Evolution of Ductile Damage

Wallin, M., Olsson, M., Ristinmaa, M. — 2008-03-12

An elasto-plastic constitutive model for porous materials is formulated within the thermodynamic framework. The formulation facilitates a natural modeling of damage as well as growth and the shrinkage of voids. Metal plasticity is used for demonstrating the possibilities of the formulation. The yield function employed is assumed to depend upon the void-volume fraction, whereas the free energy is dependent on a scalar damage field. To show the capabilities of the model the algorithmic constitutive equations are derived and implemented into a finite element program. It is shown that an extremely simple system involving only two scalar equations needs to be solved in the constitutive driver. Two numerical examples are considered: the necking of an axi-symmetric bar and localization in a notched specimen.

Numerical Modeling of Fatigue Damage and Fissure Propagation under Cyclic Loadings

Bogard, F., Lestriez, P., Guo, Y.Q. — 2008-03-12

The purpose of this work is to develop a numerical simulation procedure in order to predict the evolution of the fatigue damage and rupture in mechanical parts (such as rolling bearings and gears) under cyclic loadings. The study of the fatigue damage evolution, from the first defect appearance until the part's failure, is primordial in view of the preventive maintenance. The numerical procedure is based on the continuum damage mechanics and the thermodynamics of irreversible processes. The damage effects are fully coupled with the elasto-plastic constitutive laws on a macroscopic point of view. The Sines fatigue criterion for multiaxial stress states is used to estimate the lifetime of mechanical parts in terms of number of cycles. This numerical model is implemented into Abaqus/Explicit using an user's subroutine (Vumat). A cycle jumping algorithm allows to largely reduce the computation time. Some remeshing techniques are used to follow up the damage and rupture evolutions. The birth and the growth of the damage and rupture can be visualized via the element deleting and remeshing. These numerical tools are applied to a 2D specimen under a cyclic stretching.

A Micro Macro Approach to Modeling Progressive Damage in Composite Structures

Tay, T.E., Liu, G., Yudhanto, A., Tan, V.B.C. — 2007-12-18

Modeling progressive damage in composite materials and structures poses considerable challenges because damage is, in general, complex and involves multiple modes such as delamination, transverse cracking, fiber breakage, fiber pullout, etc. Clearly, damage in composites can be investigated at different length scales, ranging from the micromechanical to the macromechanical specimen and structural scales. In this article, a simple but novel finite-element-based method for modeling progressive damage in fiber-reinforced composites is presented. The element-failure method (EFM) is based on the simple idea that the nodal forces of an element of a damaged composite material can be modified to reflect the general state of damage and loading. This has an advantage over the usual material property degradation approaches, i.e., because the stiffness matrix of the element is not changed, computational convergence is theoretically guaranteed, resulting in a robust modeling tool. The EFM, when employed with suitable micromechanics-based failure criteria, may be a practical method for mapping damage initiation and propagation in composite structures. In this article, we present a micromechanical analysis for a new failure criterion called the strain invariant failure theory and the application of the EFM in the modeling of open-hole tension specimens. The micromechanical analysis yields a set of amplification factors, which are used to establish a set of micromechanically enhanced strain invariants for the failure criterion. The effects of material properties and volume fraction on the amplification factors are discussed.

Accumulation Damage Mode for Ferroelectric Ceramics Subjected to Mode III Fatigue Loading Conditions

Wang, B.L., Mai, Y.-W. — 2007-12-18

Based on the accumulated plastic displacement criterion, equations to predict the fatigue crack growth of piezoelectric ceramics are developed. The medium is subjected to anti-plane mechanical and in-plane electrical loads. Under such electromechanical loading conditions, it is assumed that an electric saturation zone and an elastic yielding zone near the crack tips are developed. The accumulated plastic deformation is obtained in a closed-form, which is expressed in terms of the applied loads and material constants. A fatigue crack growth law of a fourth-power function of the effective stress intensity factor is derived. The effect of electric field load on the effective crack-tip stress intensity factor and crack growth rate are shown graphically.

The Role of Interphase on Micro- to Macroscopic Responses and Prediction for Initiation of Debonding Damage of Glass Fiber Reinforced Polycarbonate

Esmaeili, N., Tomita, Y. — 2007-12-18

A computational model based on large-deformation finite element method (FEM) analysis is developed and used to evaluate the interaction between the microstructure and the heterogeneous deformation behavior of ternary composites on micro- to macroscopic scales. To uncover the influence of the plastic interphase layer on the stress—strain behavior of the three-phase system under constant strain-rate loading, the analyses of two different types of polymers with different Poisson's ratios are performed. In particular, we investigate the effects of the interphase on the normal stress at the fiber surface to predict the initiation of glass fiber—polymer matrix debonding damage. An interphase with stiffness well below that of the matrix shows a suitable effect on the micro- to macroscopic deformation behavior and suppresses the initiation of debonding, while an interphase Poisson's ratio between that of the fiber and the matrix is preferable. Furthermore, computational simulation has been performed to clarify the effects of the interphase thickness and fiber volume fraction on the normal stress at the fiber surface. The results obtained using the models suggest the realization of favorable interphase properties for suppressing the initiation of debonding at the fiber surface and improving the functionality of the reinforced polymer.

Modeling Microdefects Closure Effect with Isotropic/Anisotropic Damage

Desmorat, R., Cantournet, S. — 2007-12-18

Continuum damage mechanics (CDM) for metals is often written in terms of an isotropic (scalar) damage. In this case, solutions have been proposed to represent the differences of behavior in tension and in compression also called quasi-unilateral (QU) conditions or microdefects closure effect.

A recent anisotropic damage model has been developed to take into account the damage orthotropy induced by plasticity (Lemaitre, J., Demorat R. and Sauzay, M. (2000). Anisotropic Damage Law of Evolution, Eur. J. Mech. A/Solids, 19: 513—524). The purposes here are then two. First, a unified framework for isotropic and anisotropic damage is proposed. Then, it is to extend Ladevèze and Lemaitre's framework (Ladevèze, P. and Lemaitre, J. (1984). Damage Effective Stress in Quasi Unilateral Conditions, In: Proceedings of the 16th International Congress of Theoretical and Applied Mechanics, Lyngby, Denmark) for the QU conditions to anisotropic damage induced by plasticity.

Yield surfaces and damage versus accumulated plastic strain curves, drawn for different loading, illustrate the effect of the QU conditions on the damage evolution.