Crack-tip Triaxiality Research Articles

Experimental T33-stress formulation of test specimen thickness effect on fracture toughness in the transition temperature region

This paper describes a study of the test specimen thickness effect on fracture toughness of a material, in the transition temperature region, for CT specimens. In addition we studied the specimen thickness effect on the T 33-stress (the out-of-plane non-singular term in the series of elastic crack-tip stress fields), expecting that T 33-stress affected the crack-tip triaxiality and thus constraint in the out-of-plane direction. Finally, an experimental expression for the thickness effect on the fracture toughness using T 33-stress is proposed for 0.55% carbon steel S55C. In addition to the fact that T 33 (which was negative) seemed to show an upper bound for large B/W, these results indicate the possibility of improving the existing methods for correlating fracture toughness obtained by test specimen with the toughness of actual cracks found in the structure, using T 33-stress.

J– T characterized stress fields of surface-cracked metallic liners bonded to a structural backing – I. Uniaxial tension

Surface crack-tip stress fields in a tensile loaded metallic liner bonded to a structural backing are developed using a two-parameter J–T characterization and elastic–plastic modified boundary layer (MBL) finite element solutions. The Ramberg–Osgood power law hardening material model with deformation plasticity theory is implemented for the metallic liner. In addition to an elastic plate backed surface crack liner model, elastic–plastic homogeneous surface crack models of various thicknesses were tested. The constraint effects that arise from the elastic backing on the thin metallic liner and the extent to which J–T two parameter solutions characterize the crack-tip fields are explored in detail. The increased elastic constraint imposed by the backing on the liner results in an enhanced range of validity of J–T characterization. The higher accuracy of MBL solutions in predicting the surface crack-tip fields in the bonded model is partially attributed to an increase in crack-tip triaxiality and a consequent increase in the effective liner thickness from a fracture standpoint. After isolating the effects of thickness, the constraint imposed by the continued elastic linearity of the backing significantly enhanced stress field characterization. In fact, J and T along with MBL solutions predicted stresses with remarkable accuracy for loads beyond full yielding. The effects of backing stiffness variation were also investigated and results indicate that the backing to liner modulus ratio does not significantly influence the crack tip constraint. Indeed, the most significant effect of the backing is its ability to impose an elastic constraint on the liner. Results from this study will facilitate the implementation of geometric limits in testing standards for surface cracked tension specimens bonded to a structural backing.

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.

Comparison of cohesive zone parameters and crack tip stress states between two different specimen types

The cohesive zone parameters (separation energy and cohesive strength) and the crack tip triaxialities are compared between a compact tension (CT) and a double edge notched tension (DENT) specimen with smooth side-surfaces. The material is a pressure vessel steel 20MnMoNi55. The cohesive zone parameters are determined by fitting the simulated crack extensions near the midsection to the experimental data. The purpose of the study is to understand the relationship between the cohesive zone parameters and the crack tip stress triaxiality. The results show that for the same cohesive zone parameters the crack tip triaxiality near the midsection is lower in DENT specimens than in CT specimens. When the separation energy is set constant for CT and DENT specimens, the cohesive strength for the DENT specimens should be significantly lower than that for the CT specimens in order to make the simulated crack extensions near the midsection fit to the experimental data. Near the midsection, the cohesive strength and crack tip triaxiality influence each other: the specimen with a higher stress triaxiality has a higher cohesive strength; an increase of cohesive strength results in an increase of the crack tip triaxiality.

Fracture behavior of polyetherimide (PEI) and interlaminar fracture of CF/PEI laminates at elevated temperatures

AbstractTo investigate the effects of environmental temperature on fracture behavior of a polyetherimide (PEI) thermoplastic polymer and its carbon fiber (CF/PEI) composite, experimental and numerical studies were performed on compact tension (CT) and double cantilever beam (DCB) specimens under mode‐I loading. The numerical analyses were based on 2‐D large deformation finite element analyses (FEA). Elevated temperatures greatly released the crack tip triaxiality (constraint) and promoted matrix deformation due to low yield strength and enhanced ductility of the PEI matrix, which resulted in the greater plane‐strain fracture toughness of the bulk PEI polymer and the interlaminar fracture toughness of its composite during delamination propagation with increasing temperature. Furthermore, the high triaxiality was developed around the delamination front tip in the DCB specimen, which accounted for the poor translation of matrix toughness to the interlaminar fracture toughness by suppressing the matrix deformation and reducing the plastic energy dissipated in the plastic zone. Especially, at delamination initiation, the weakened fiber/matrix adhesion at elevated temperatures led to premature failure of fiber/matrix interface, suppressing matrix deformation and preventing the full utilization of matrix toughness. Consequently, low interlaminar fracture toughness was obtained at elevated temperatures. POLYM. COMPOS., 26:20–28, 2005. © 2004 Society of Plastics Engineers.

Prediction of stable crack growth in surface cracked plate of Aluminum 7050 alloy

To simulate stable crack growth, three-dimensional finite element analysis using the constant Crack Tip Opening Angle (CTOA) fracture criterion was performed for a thin plate made of Aluminum 7050 alloy. The critical CTOA value was experimentally obtained by the Rubber Impression Method, which directly measures the three-dimensional crack profiles by inserting the gel-state silicon rubber into the crack, and taking out the solid-state rubber later. From the microscopic observation from the broken specimen, it was found that, as the crack extends, the amount of crack growth near the free surface is more than that in the depth/thickness direction, which creates the special tunneling, e.g., canoe-shaped crack extension. For the numerical simulation, the surface-cracked plate was analyzed by quasi-static elastic-plastic finite strain analysis with the node release and the reloading technique. Consistent with experimental observations, numerical simulation with constant CTOA fracture criteria produced tunneling of a surface crack, but the shape of the crack front deviated from the experimental crack front as the free surface was approached. To address the local crack tip constraint effect on the stable crack growth, various fracture parameters - crack tip triaxiality, equivalent plastic strain, and void growth ratio as the crack extends – were also investigated.

Numerical and experimental studies on the fracture behavior of rubber-toughened epoxy in bulk specimen and laminated composites

To study the toughening mechanisms of liquid rubber (LR) and core-shell rubber (CSR) in bulk epoxy and composite laminate, experimental and numerical investigations were carried out on compact tension (CT) and double-cantilever-beam (DCB) specimens under mode-I loading. The matrix materials were pure epoxy (DGEBA), 15% LR (CTBN) and 15% CSR modified epoxies. Experimental results and numerical analyses showed that both liquid rubber (LR) and core-shell rubber (CSR) could improve significantly the fracture toughness of pure epoxy (DGEBA). However, the high toughness of these toughened epoxies could not be completely transferred to the interlaminar fracture toughness of the unidirectional carbon fibre reinforced laminate. The main toughening mechanism of CSR in bulk epoxy was the extensive particle cavitation, which greatly released the crack-tip triaxiality and promoted matrix shear plasticity. The poor toughness behavior of CSR in the carbon fibre laminate was thought to be caused by the high constraint imposed by the stiff fibre layers. No particle cavitation had been observed in LR modified epoxy and the main toughening mechanism was merely the large plastic deformation near the crack-tip due to the rubber domains in the matrix which results in a lower yield strength but a higher elongation-to-break.

Effect of rubber functionality on microstructures and fracture toughness of impact-modified nylon 6,6/polypropylene blendsPart II. Toughening mechanisms

Toughening mechanisms in blends containing 60 parts nylon 6,6, 20 parts polypropylene (PP) and 20 parts styrene–ethylene/butylene–styrene (SEBS) grafted to different levels of maleic anhydride (MA) were investigated. The sequence of events was carefully characterised using different microscopic techniques. It was found that under triaxial constraint interfacial cavitation followed by multiple crazing and subsequently massive shear yielding of the matrix contributed to an enormous toughening effect in core-shell microstructures observed in 0.92%-maleated blend (0.74% in Part I paper [Wong SC, Mai Y-W. Polymer, 1999;40:1553], should be 0.92% as corrected in this paper). The core-shell structure was formed when the spherical domains of PP were surrounded by SEBS rubber in a nylon-rich matrix.. In this composition, miscibility between the dispersed SEBS-g-MA and the nylon phase was maximised as revealed by thermal-mechanical analysis. The SEBS was most effective in toughening the nylon/PP blends when it cavitated to introduce ligament bridges between debonded PP particles at the crack tip. Interfacial cavitation and multiple crazing served to relieve the hydrostatic tension ahead of crack growth and subsequently enhanced the shear-yielding component of stresses in the matrix material. Other blend compositions that did not show controlled cavitation resulted in little plastic flow surrounding the crack tip and reduced fracture toughness. These results reinforced the notion that cavitation of SEBS at the nylon–PP interface was an essential mechanism to promote toughening in materials subjected to high crack tip triaxiality.

Stress triaxiality constraint and crack tip parameters

A relationship between crack tip constraints of specimens and those defined by the Hutchinson-Rice-Rosengren (HRR) solution in the plane strain case has been derived from the corrected stress-strain field presented by Anderson, by taking account of losses in triaxiality of specimens. An analytical expression has been established and verified which describes a sufficient and necessary condition for the validity of a single parameter characterizing crack tip stresses; namely the crack tip triaxiality constraints defined by the single parameter should be satisfied by those of specimens. The simple correction for crack tip stresses proposed by Anderson has been extended to situations of different specimen geometry. Furthermore, a new elastic-plastic fracture criterion, including the effect of crack tip triaxiality on the parameter characterizing fracture, has been developed and proven to be a material constant independent from specimen geometry for a given material state. It has also been demonstrated that it is impossible to obtain the plane strain fracture toughness J IC directly from laboratory test specimens because the crack tip triaxiality constraints required by the HRR solution cannot be met for various specimens.

Crack tip parameters for large scale yielding and low constraint configurations

This article introduces a quasi-deformation plasticity theory which takes account of nonproportional loading by means of an orthotropic yield surface. The analysis is used to extend fracture mechanics concepts beyond the normal limits of J-integral theory. A simple correction for crack tip stresses is derived from the quasi-deformation assumption. This correction indicates that the degree of crack tip triaxiality is related to the relationship between the J-integral and the crack tip opening displacement (CTOD). Predictions of crack tip stress fields agree well with published finite element results.