Damage development in a sidegrooved CT specimen based on a 3-D endochronic damage model

This paper presents a three-dimensional crack initiation analysis in a sidegrooved CT specimen. This is achieved with an endochronic damage model proposed recently by Chow and Chen [ 1,2] and discretized for finite element analysis. The damage model enables the quantification of the progressive damage evolution which would not be otherwise possible using the conventional fracture mechanics analysis. By employing two separate damage failure criteria, the crack is predicted to initiate at a small distance from the sidegroove and the prediction agrees well with the experimental observation. A more uniform crack initiation across the crack-tip line is observed both experimentally and theoretically relative to the CT specimen without sidegrooving. 1. In troduct ion In an earlier investigation, nonuniform crack initiation along the crack-tip front producing a tunneling phenomenon was observed experimentally in CT specimens without sidegroove, [3]. The extent of tunneling increased with crack growth. The crack was predicted to first initiate at the middle of the crack-tip line for a CT specimen without sidegroove with the endochronic damage analysis [3]. From both experimental and numerical results, it was found that the specimen thickness had a definite influence on the stress state, damage evolution and the crack initiation load. These phenomena result from the nonuniform stress state across the thickness due to different deformation constraints. In fracture toughness testing, the thickness of the test specimens should be large enough to ensure that the majority of the specimen thickness deforms in plane strain mode and the distribution of the stress state is uniform over most of the interior part. This is to ensure that maximum uniformity of the crack-tip profile can be achieved. In reality, one of the important factors influencing the crack initiation load is the stress state or deformation constraint at the crack tip. In standard fracture toughness test specimens, the stress state near and at the two side surfaces is in plane stress and approaches to plane strain towards the interior part of the specimen. There is therefore a transition region between the surface plane stress deformation mode and the interior plane strain deformation mode if the plane strain region exists. When the specimen thickness is large enough, the majority of the interior of the thickness is in the plane strain deformation mode, thus producing uniform crack propagation over most of the interior part. If the stress state could be created to be almost uniform along the crack-tip profile in some other ways, then uniform crack initiation across the thickness could also be obtained without requiring the use of larger specimen thickness. DeLorenzi and Shih [4] and Shih et al. [5] studied the fracture behavior of sidegrooved fracture specimens. It was found that the unifrom crack propagation profile can be obtained with a sidegrooved specimen and the crack initiation load in plane strain condition can also be obtained with a smaller specimen with sidegroove. 210 C.L. Chow and X.E Chen Obviously the effects of sidegrooves are localized, so that some associated problems should be discussed when global parameters such as J are employed to analyze the fracture behavior. Firstly J is defined in a plane perpendicular to the crack front line. For a sidegrooved specimen, the deformation mode is different in the plane where J is defined. In the crack extension line where the deformation in the thickness direction is constrained by the bulk material above and below the sidegroove, the deformation mode is quite different from that in other parts remote from the sidegroove. Actually, the J 's applicability in fracture analysis depends on the J-dominant fields in the crack-tip regions. This could be achieved for power law hardening material when certain size requirements of fracture specimens without sidegroove are satisfied. But for the CT specimen with sidegroove, especially at the close proximity of the sidegroove where the deformation constraint change abruptly at crack initiation, the J-dominance in this case becomes questionable. Another important phenomenon which is not considered in the conventional fracture mechanics based analysis, is the damage development at the crack tip that can result in considerable stress redistribution and its associated stiffness change. In this paper, a CT specimen with sidegroove is analyzed using an endochronic damage model. The material used was 2024-T351 aluminum alloy of thickness 12.7 mm. The constitutive equations to describe the material behavior incorporate the endochronic theory of plasticity coupled with anisotropic damage. A three-dimensional finite element program employing the constitutive equations has been developed to evaluate distributions of the stress, strain and damage, etc. As the damage evolution and damage effects are included in the analysis, the progressive material deterioration and failure process in the crack tip are obtained, which would not otherwise be possible using the conventional fracture mechanics analysis. 2. An endochronie damage theory The constitutive equations used in this study are based on an endochronic theory of plasticity coupled with anisotropic damage. The plastic damage model introduces the effective stress and the effective strain. The intrinsic time is defined in the effective plastic strain space as [1,2] d~ d z f (~) , (1) d ~ = (deP'd-eP) 1/2, (2) where f ( ( ) is the hardening function, which is chosen as 1 + /~( where/3 is a material constant. With the introduction of yielding surface, the incremental elastoplastic stress-strain relationship is [3, 6, 7, 8] dS= 2/zo(d~ d~ p) + Ao(I:d~)I = 2#od~ + Ao(I:d~)I2#o(Sr ) ( (Sr)" d~) C(So)2f2(() ' (3)