Examination of Consistent Application of Interfacial Fracture Energy Versus Mode-Mixity Curve for Delamination Prediction

Experimentally characterized critical interfacial fracture energy is often written as an explicit trigonometric function of mode-mixity and is used to determine whether an interfacial crack will propagate or not under given loading conditions for an application. A different approach to assess whether an interfacial crack will propagate is to employ a failure locus consisting of the critical fracture energies corresponding to different fracture modes, represented by an implicit formulation. Such a failure locus can be linear, elliptical, among other shapes. As it is nearly impossible to obtain isolated GIc or GIIc values through experimentation, extrapolations are used to determine these two extreme values based on intermediate experimental data. However, the magnitude of these extreme values as well as the shape of the two forms of failure curves are at risk of being inconsistent should proper care not be taken. An example of such an inconsistency would be to use a trigonometric formulation to obtain the extreme values through extrapolation and then employ those values in simulation through an elliptical failure. In this work, we have employed a series of commonly used interfacial fracture energy measurement techniques over a range of mode-mixities for a metal/polymer interface to demonstrate the potential discrepancy in the two approaches and to underscore the need for a consistent approach in evaluating interfacial crack propagation.

On Phenomenological Failure Loci of Metals under Constant Stress States of Combined Tension and Shear: Issues of Coaxiality and Non-Uniqueness

The present study investigates how the choice of characterization test and the composition of the stress state in terms of tension and shear can produce a non-unique failure locus in terms of stress triaxiality under plane stress conditions. Stress states that are composed of tensile and simple shear loadings result in a loss of proportionality between the cumulative strain and stress such that the principal frames become non-coaxial despite a constant stress triaxiality. Consequently, it is shown that the conventional interpretation of a failure locus in plane stress is based upon an implicit assumption of proportional coaxial loading. The use of simple shear tests along with traditional in-plane tensile tests for fracture characterization is only one “path” that can be taken in terms of the stress triaxiality, which may produce a bifurcation at uniaxial tension while the tension–torsion path does not. In general, the failure locus in terms of the equivalent strain is a failure surface and must consider the composition of the stress state that produces a given triaxiality. A comprehensive review of phenomenological fracture loci within a modified Mohr-Coulomb (MMC) framework is performed to highlight how the choice of stress states obtained using different characterization tests can change the apparent fracture locus of a material. The finite strain solutions for the work conjugate equivalent strain are derived for various loading paths that produce the same stress triaxiality. It is then shown that accounting for non-coaxiality leads to equivalent failure strains that are even higher than previously reported in tension–torsion tests within the literature. The equivalent plastic strains integrated from finite-element simulations are work-conjugate by definition. The equivalent strains estimated from the cumulative principal strains using DIC strain measurement depend upon a coaxial or non-coaxial assumption. Finally, an analytical solution for the onset of diffuse necking that accounts for the stabilizing influence of shear loading against a tensile instability is considered. Even under plane stress conditions, a failure surface arises in terms of the equivalent strain at necking, the stress triaxiality, and the severity of shear loading.

Micromechanics-based prediction of the failure locus of angle-ply laminates subjected to biaxial loading

A mesoscale finite element model is presented for calculating the deformation and initial strength of angle-ply laminates subjected to biaxial tension and biaxial tension–compression. Using the concept that the whole laminate structure can be represented by a rhombohedral unit cell, predictions of the mechanical behavior for various biaxial loading ratios are made. Damage by microcracking at the fiber–matrix interface and shear band formation in the matrix are incorporated into the numerical simulations. The failure locus calculated from the mesoscale model is found to agree with experimental data available in the literature better than do theoretical predictions. Results of this study indicate that computational micromechanics can be used for detecting leakage failure in filament wound tubes.

The Sensitivity to the Lode Parameter in Ductile Failure of Tubular Steel Grades

Ductile failure in steels is highly controlled by the stress state, characterized by the stress triaxiality (T) and the Lode parameter (L). The ASME Boiler and Pressure Vessel Code requires pressure vessels to be designed to resist local ductile failure. However, the standard does not account for the Lode parameter dependence in its failure locus. In this study, the influence of the stress state, characterized T and L, on the ductility of ASME tubular product steel grades is investigated. Two seamless pipes of midstrength carbon steel SA-106 Gr. B and high-strength superduplex steel SA-790 were considered. Ring specimen geometries for plane strain (PS) stress state (L = 0) and tensile stress (TS) state (L = −1) are utilized to establish the ductile failure locus in terms of T and L for the two steels. The experimental results (EXP) show that the effect of the Lode parameter on the failure locus for the SA-106 Gr. B steel is insignificant, whereas for the SA-790 steel, the effect is rather significant. A parameter SL is introduced in order to quantify the sensitivity of the failure locus to the Lode parameter. It is found that for materials with ultimate strength lower than about 550 MPa, the sensitivity to L is insignificant (SL ≈ 1), whereas for materials with ultimate strength higher than 550 MPa, the sensitivity to L could be significant (SL > 1). Scanning electron microscopic (SEM) analysis of the fracture surfaces revealed that the sensitivity to L is closely associated with the rupture micromechanisms involved.

New Ring Specimen Geometries for Determining the Failure Locus of Tubulars

Pressure vessels designed in accordance with the ASME BPVC code are protected against local ductile failure. Recent work has shown that local ductile failure highly depends on the stress state characterized by both stress triaxiality (T) and the Lode parameter (L). In this paper, the effect of stress state on the ductility of a tubular steel is studied. Two ring specimen configurations were optimized to allow the determination of the ductile failure locus at both tensile and plane strain loadings. The geometry of both ring specimen configurations was optimized to achieve a plane strain (L=0) condition and a generalized tension (L=-1) condition. Notches with different radii were machined on both types to achieve a wide range of stress triaxiality. Specimens were manufactured from SA-106 carbon tubular steel and were tested to determine the ductile failure loci as a function of T and L. Failure locus of SA-106 steel was constructed based on the failure instants and was found to be independent of the Lode parameter. The ASME-BPVC local failure criterion showed close agreement with experimental results (EXP).

An Experimental Setup for Determining the Failure Locus of ASME Tubular Pressure Vessel Steel Grades

Pressure vessels designed in accordance with the ASME BPVC code are protected against local ductile failure. Recent work has shown that local ductile failure highly depends on the stress state characterized by both stress triaxiality (T) and the Lode parameter (L). In this paper, the effect of stress state on the ductility of a tubular steel is studied. Two ring specimen configurations were optimized to allow the determination of the ductile failure locus of both tensile and plane strain loadings. The geometry of both ring specimen configurations was optimized to achieve a plane strain (L = 0) condition and a generalized tension (L = −1) condition. Notches with different radii were machined on both types to achieve a wide range of stress triaxiality levels. Specimens were manufactured from SA-106 carbon tubular steel and were tested to determine the ductile failure loci as a function of T and L. Failure locus of SA-106 steel was constructed based on the failure instants and was found to be independent of the variation in the Lode parameter. The ASME-BPVC local failure criterion showed close agreement with experimental results.

Determination of Parameters for the Damage Mechanics Approach to Ductile Fracture Based on a Single Fracture Mechanics Test

The local approach to modelling ductile tearing is a useful technique to give insight into fracture mechanics. However, applications of the local approach have been stymied by the high cost of finding the parameters that characterize it because of the number of specimens and expensive post-processing that the testing requires. In this paper, a novel iterative method to extract a failure locus from one Crack Tip Opening Displacement (CTOD) specimen is presented. Material points fail under various different stress states in a CTOD specimen, so many different points on the failure locus can be found through thoughtful post-processing in FEA. A phenomological ductile failure locus is fitted through the stress triaxiality, Lode angle, and plastic strains that cause failure at material points in the CTOD test. Simulating a CTOD test with a different aspect ratio has shown that the failure locus found by this method can be predictive, giving both accurate force versus Crack Mouth Opening Displacement (CMOD) curves and realistic fracture surfaces featuring separate tunnelling and shear lips.

Ring Specimen Geometry for Determining the Ductility of Tubulars

Pressure vessels designed in accordance with the ASME BPVC code are protected against local ductile failure. Recent work has shown that local ductile failure highly depends on the stress state characterized by both stress triaxiality (T) and the Lode parameter (L). In this paper, the effect of stress state on the ductility of a tubular steel is studied. Two ring specimen configurations were optimized to allow the determination of the ductile failure locus of both tensile and plane strain loadings. The geometry of both ring specimen configurations was optimized to achieve a plane strain (L = 0) condition and a generalized tension (L = −1) condition. Notches with different radii were machined on both types to achieve a wide range of stress triaxiality. Specimens were manufactured from SA-106 carbon tubular steel and were tested to determine the ductile failure loci as a function of T and L. Failure locus of SA-106 steel was constructed based on the failure instants and was found to be independent of the variation in the Lode parameter. The ASME-BPVC local failure criterion showed close agreement with experimental results.