C.L. Chow

An anisotropic theory of continuum damage mechanics for ductile fracture

Abstract The development of an anisotropic theory of continuum damage mechanics for ductile fracture is described. A new anisotropic damage evolution equation and a constitutive equation of plasticity are formulated using a damage effect tensor M(D) proposed recently by the authors. This is followed by the development of a generalized damage characteristic tensor J to characterize anisotropic damage evolution which is shown to be compatible with the damage effect tensor. The tensorial equation of damage evolution for the proposed tensor J can be reduced to a scalar equation if the damage state is isotropic. Verification of the proposed model has been performed by conducting simple tension tests and the results are shown to be satisfactory.

On evolution laws of anisotropic damage

Abstract This paper is focused on the development of evolution laws of anisotropic damage. Material damage in the form of microcracks and microcavities leading to macro-mechanical property variations is modelled phenomenologically with some distortion and blurring of fine details, arguing that the extent of material property changes may serve as an appropriate, indirect measure of damage. The experimentally observed phenomenon of damage hardening is also described. The well-established thermodynamic theories of irreversible processes are then appealed for deriving constitutive equations of the materials suffering from progressive deterioration, together with a new hypothesis of energy equivalence instead of the restrictive hypothesis of strain or deformation equivalence hitherto proposed. Thermodynamic conjugate force of the damage variable, the “damage energy release rate”, is deduced in analytical form by assuming that the energy involved in the plastic flow and damaging processes can be uncoupled. Evolution laws of anisotropic damage are established following the concept of a damage surface in the space of affinities as well as the principle of maximum damage dissipation. An important outcome of the investigation is the identification of a new damage characteristic tensor J which can accurately describe the anisotropic nature of damage growth and yet is simple with only one unknown parameter to be determined from a standard tension test.

Ductile fracture characterization with an anisotropic continuum damage theory

Abstract The paper presents an investigation of characterizing ductile fracture of centre-cracked tension specimen made of thin aluminium alloy based on the theory of an anisotropic continuum damage. The characterization is achieved by predicting the crack initiation of the ductile specimen using the finite element analysis. The computed stress/strain distributions are also compared with those using a fracture mechanics approach. The comparison reveals the underestimation of the computed stresses, resulting an over-estimation of fracture load using the conventional fracture mechanics analysis. Centre-cracked tension specimens are manufactured along both the longitudinal and transverse rolling direction in order to examine the effect of the rolling induced material anisotropy on the fracture load. The test results indicate that there is approximately an 8.8% difference in the measured fracture loads due to the effect of the rolling process, although the difference is not considered significant. The average fracture load measured from a total of twelve test specimens is 276.3 MPa which is compared favourably with the computed fracture load of 260 MPa based on the proposed anisotropic damage model and of 290 MPa based on a conventional fracture mechanics approach.

On crack initiation angle of mixed mode ductile fracture with continuum damage mechanics

Abstract This paper presents the development and examination of two fracture criteria proposed for predicting the crack initiation angle in mixed mode ductile fracture based on the theory of continuum damage mechanics. The criteria are deduced respectively from the postulates that 1. (1) a crack propagates at the direction where the ratio of the effective damage equivalent stress \ gs d and the effective plastic equivalent stress \ gs p reaches its maximum or Max [ C(θ) ] for which C = \ gs d / \ gs p , 2. (2) a crack propagates at the direction of maximum effective damage equivalent stress \ gs d . The criteria are used to predict the angles of crack initiation in mixed mode specimens made of aluminium alloy 2024-T3. The thin aluminium plates embedded with an isolated crack of inclined angle β = 30, 45, 60 and 75° are manufactured to simulate mixed mode fracture. In order to investigate the effects of material anisotropy, the mixed mode specimens are produced both parallel to and, transverse from the rolling direction. A finite element analysis based on the anisotropic model of continuum damage mechanics theory proposed earlier by the authors is performed and the angles of crack initiation of the five mixed mode specimens predicted using the proposed fracture criteria and the strain energy density criterion based on the conventional fracture mechanics. The angles of predicted crack initiation based on the proposed fracture criteria not only agree satisfactorily with those determined experimentally but also offer overall better accuracy as compared with those predicted using the conventional fracture mechanics approach. In addition, there is a definite, although not significant, effect of the material anisotropy on the measured crack initiation angles.

Subcritical crack growth in ductile fracture with continuum damage mechanics

Abstract The anisotropic model of continuum damage mechanics proposed recently by the authors is extended to characterize subcritical crack growth in thin aluminium alloy sheets undergoing gross plastic deformation. This is achieved by developing a subcritical crack propagation model incorporated in a finite element formulation applicable to non-proportional loading conditions. The predicted fracture loads and incremental crack growths are compared satisfactorily with those determined experimentally. The investigation also confirms the accuracy and convergency of the proposed model, as the predicted results are found to be more accurate using a fine finite element network as compared with those from a coarse network reported earlier. In addition, the fracture loads computed based on the theory of proportional loading are found to be much too conservative due to the unloading effect in the crack tip region causing the abrupt change of the direction of principal stress at each crack advance.

A unified formulation of fatigue crack propagation in aluminum alloys and PMMA

Abstract Based on the quasistatic energy analysis, a unified formulation of fatigue crack propagation capable of characterizing aluminum alloys of Type 7075-T6 and 2024-T3 and polymethylmethacrylate (PMMA) is described. The formulation is deduced from the strain energy release rate consideration, which is shown to be inherently capable of taking into account the mean stress effect at both Stage II and Stage III crack growth of the materials.

Fatigue crack propagation in mild steel

Abstract An investigation of the applicability of a unified formulation to include fatigue crack propagation (FCP) of mild steel is examined. The formulation recently proposed by the authors has been found to be capable of characterizing aluminium alloys and PMMA. The mean stress ratios chosen for the investigation varied from 0.1 to 0.7 at increments of 0.2 each. While both Pariss and Formans formulations fail to satisfactorily characterize the combined FCP rates of mild steel, aluminium alloys and PMMA, the proposed formulation yields an excellent coefficient of correlation of 0.976 for the materials, and proves once again the applicability and validity of the FCP formulation.

Hysteretic effects of damage and stress on ductile fracture characterization

Abstract A significant phenomenon known as hysteretic effect resulting from the damage evolution of material degradation upon loading observed in the stress analysis based on the theory of continuum damage mechanics is the structural response to the relative rotational change of principal stress and damage planes. No such observation is identified in the conventional stress analysis. This paper presents an investigation of highlighting the hysteretic effects on the fracture behaviors of the mixed mode fracture plates of β = 90, 75, 60, 45 and 30° . While the hysteresis is confined to 15° for the plates analysed under the proportional loading, the magnitude is markedly increased under the arbitrary or non-proportional loading which often occurs in engineering structures. In addition, a new fracture criterion known as δ- criterion which is defined by the angle of the radial and principal damage planes in a material element is proposed to determine the angle of crack initiation for the mixed mode plates and found to be in satisfactory agreement with experimental observations.

DAMAGE FIELD AND ITS EVOLUTION IN A GLASS-FIBER CLOTH/EPOXY COMPOSITE PLATE WITH A CENTRAL HOLE

Abstract Because of damage which can result in the change of material behavior, the actual stress-strain field of the damaged material will be obviously different from the ideal stress-strain field in the undamaged composite under loading. Description of the damage field and its evolution is a very important problem for research on strength and failure of composite structure. The displacement field and the corresponding strain field of a glass-fiber cloth/epoxy composite plate subjected to tension loading were measured by using Moire interferometry. The change of the damage variable field, the elasticity field, the real stress field, the damage energy dissipation rate field and their evolution can be then determined based on the continuum damage theory in this paper.

Ductile crack propagation with the strain-energy density criterion

The strain energy density criterion is used to characterize subcritical crack growth in a thin aluminum alloy sheet undergoing general yielding. A finite element analysis which incorporates both material and geometrical nonlinear behaviors of the cracked sheets is developed to predict fracture loads at varying crack growth increments. The predicted results are in excellent agreement with those measured experimentally, thus confirming the validity of the strain energy density criterion for characterizing ductile crack propagation.