Crack paths under mixed mode loading

Long fatigue cracks that initially experience mixed mode displacements usually change direction in response to cyclic elastic stresses. Eventually the cracks tend to orient themselves into a pure mode I condition, but the path that they take can be complex and chaotic. In this paper, we report on recent developments in techniques for tracking the crack path as it grows and evaluating the strength of the mixed mode crack tip stress field

Determination of stress intensity factors for interface cracks under mixed-mode loading

A simple technique was developed using conventional finite element analysis to determine stress intensity factors, K1 and K2, for interface cracks under mixed-mode loading. This technique involves the calculation of crack tip stresses using non-singular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating three different bimaterial combinations. For the normal loading case, the K's were within 2.6 percent of an exact solution. The normalized K's under shear loading were shown to be related to the normalized K's under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from knowledge of the K's under normal loading. The equation was verified by computing the K's for a mixed-mode case with equal and normal shear loading. The correlation between exact and finite element solutions is within 3.7 percent. This study provides a simple procedure to compute K2/K1 ratio which has been used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/K1 ratios could be used to fully characterize interface fracture toughness

A mixed-mode bending apparatus for delamination testing

A mixed-mode delamination test procedure was developed combining double cantilever beam mode I loading and end notch flexure mode II loading on a split unidirectional laminate. By loading the specimen with a lever, a single applied load simultaneously produces mode I and II bending loads on the specimen. This mixed mode bending (MMB) test was analyzed using both finite element procedures and beam theory to calculate the mode I and II components of strain energy release rate, G sub I and G sub II, respectively. The analyses showed that a wide range of G sub I/G sub II ratios could be produced by varying the applied load position on the loading lever. As the delamination extended, the G sub I/G sub II ratios varied by less than 5 percent. The simple beam theory equations were modified to account for the elastic interaction between the two arms of the specimen and to account for shear deformations. The resulting equations agreed closely with the finite element results and provide a basis for selection of G sub I/G sub II test ratios and a basis for computing the mode I and II components of measured delamination toughness. The MMB specimen analysis and test procedures were demonstrated using unidirectional laminates

Crack front instabilities under mixed mode loading in three dimensions

The evolution of a crack front under mixed mode loading (I+III) is studied using a phase field model in 3 dimensions with no stress boundary conditions. As previously observed experimentally in gels, there is a relaxation toward a geometry where $K_{III}=0$ without any front fragmentation even for high values of the initial mode mixity $K_{III}/K_{I}$. The effects of the initial condition is studied and it is shown that irregularities in the initial slit can lead to front fragmentation for smaller values of the ratio $K_{III}/K_{I}$ as is observed in experiments.Comment: 6 pages, 7 figures, accepted for publication in EuroPhysics Letter

Characterization of mode 1 and mixed-mode failure of adhesive bonds between composite adherends

A combined experimental and analytical investigation of an adhesively bonded composite joint was conducted to characterize both the static and fatigue beyond growth mechanism under mode 1 and mixed-mode 1 and 2 loadings. Two bonded systems were studied: graphite/epoxy adherends bonded with EC 3445 and FM-300 adhesives. For each bonded system, two specimen types were tested: a double-cantilever-beam specimen for mode 1 loading and a cracked-lapshear specimen for mixed-mode 1 and 2 loading. In all specimens tested, failure occurred in the form of debond growth. Debonding always occurred in a cohesive manner with EC 3445 adhesive. The FM-300 adhesive debonded in a cohesive manner under mixed-mode 1 and 2 loading, but in a cohesive, adhesive, or combined cohesive and adhesive manner under mode 1 loading. Total strain-energy release rate appeared to be the driving parameter for debond growth under static and fatigue loadings

Simulation of dynamic delamination and mode I energy dissipation

Delamination initiation and propagation of aeronautic composites is an active field of research. In this paper we present a methodology for critical energy release rate correlation of numerical simulation and experimental data. Experiments of mode I critical energy release rate were carried out at quasi static and pseudo dynamic loading rates. Cohesive finite elements are used to predict the propagation of delamination in a carbon fiber and epoxy resin composite material. A bilinear material model is implemented via user defined cohesive material subroutine in LS-DYNA. The influence of mode I energy release rate in mixed mode loading, due to a low velocity impact, is also investigate

Effects of stitching on delamination of satin weave carbon-epoxy laminates under mode I, mode II and mixed-mode I/II loadings

The objective of the present study is to characterize the effect of modified chain stitching on the delamination growth under mixed-mode I/II loading conditions. Delamination toughness under mode I is experimentally determined, for unstitched and stitched laminates, by using untabbed and tabbed double cantilever beam (TDCB) tests. The effect of the reinforcing tabs on mode I toughness is investigated. Stitching improves the energy release rate (ERR) up to 4 times in mode I. Mode II delamination toughness is evaluated in end-notched flexure (ENF) tests. Different geometries of stitched specimens are tested. Crack propagation occurs without any failure of stitching yarns. The final crack length attains the mid-span or it stops before and the specimen breaks in bending. The ERR is initially low and gradually increases with crack length to very high values. The mixedmode delamination behaviour is investigated using a mixed-mode bending (MMB) test. For unstitched specimens, a simple mixed-mode criterion is identified. For stitched specimens, stitching yarns do not break during 25% of mode I ratio tests and the ERR increase is relatively small compared to unstitched values. For 70% and 50% of mode I ratios, failures of yarns are observed during crack propagation and tests are able to capture correctly the effect of the stitching: it clearly improves the ERR for these two mixed modes, as much as threefold

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

© 2015 Elsevier Ltd. All rights reserved.This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micro-mechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibulls criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the internal Z-pin splitting are discussed. The primary aim is to develop a robust numerical tool and guidelines for designing Z-pins with optimal bridging behaviour

Mixed-mode cyclic debonding of adhesively bonded composite joints

A combined experimental-analytical investigation to characterize the cyclic failure mechanism of a simple composite-to-composite bonded joint is conducted. The cracked lap shear (CLS) specimens of graphite/epoxy adherend bonded with EC-3445 adhesive are tested under combined mode 1 and 2 loading. In all specimens tested, fatigue failure occurs in the form of cyclic debonding. The cyclic debond growth rates are measured. The finite element analysis is employed to compute the mode 1, mode 2, and total strain energy release rates (i.e., GI, GII, and GT). A wide range of mixed-mode loading, i.e., GI/GII ranging from 0.03 to 0.38, is obtained. The total strain energy release rate, G sub T, appeared to be the driving parameter for cyclic debonding in the tested composite bonded system

Lifetime evaluation of concrete structures under sustained post-peak loading

Experimental tests on crack propagation in concrete under constant post-peak loading are simulated using the finite element method and the cohesive crack model, in both Mode I and Mixed-mode conditions. The time-dependent behaviour of concrete in the process zone is due to the interaction and growth of microcracks, a phenomenon which, for high constant load levels, turns out to be predominant over linear viscoelastic creep in the bulk material. In mechanical systems based on this type of material behaviour (creep and strain-softening taking place simultaneously), the initial value problem is non-parabolic, i.e., the error at one time level is affected by the accumulation of errors introduced at earlier time levels. Despite these difficulties, the scatter in numerical failure lifetime vs. load level turns out to be negligible in Mode I conditions and practically acceptable in Mixed-mode conditions. Therefore the time-dependent behaviour of the process zone can be inferred solely from the results of direct tensile tests