Bent F. Sørensen

Determination of cohesive laws by the J integral approach

Abstract The determination of cohesive laws for describing large scale failure process zones is discussed. Firstly, a general approach for determination of cohesive laws, by the measurement of the J integral and end-opening of the cohesive zone of double cantilever beam specimens loaded with pure bending moments, is described. Next, two case stories are reviewed: failure of adhesive joints and splitting of a unidirectional carbon fibre/epoxy composite. For the adhesive joints, measured failure strengths of bonded panels having a central notch were found to in very good agreement with predictions from cohesive law parameters determined on test specimens. For the problem of splitting of unidirectional composites, micromechanisms were observed in situ during cracking. A cohesive law shape, predicted by a micromechanics model, was found to agree well with macroscopic cohesive law determined by the J integral approach. The cohesive law was used for predicting effect of specimen shape on strength; predictions were confirmed by experiments. Finally, some ideas regarding determination of mixed mode cohesive laws are discussed.

Large-scale bridging in composites: R-curves and bridging laws

Abstract Large-scale bridging was studied experimentally in a unidirectional carbon fibre/epoxy matrix composite material. For intralaminar cracks a significant increase in the crack growth resistance occurred with increasing crack extension. The increase in the crack growth resistance was attributed to fibre cross-over bridging. The R-curve behaviour, i.e. the relationship between crack growth resistance and crack extension depended on specimen geometry. Therefore, R-curves are not material properties when large-scale bridging occurs. The bridging law (the relationship between the local crack opening δ and the local bridging traction σ ) was measured. The bridging law was found to be independent of specimen geometry. A bridging law can therefore be used as a material property in composites with large-scale bridging. The bridging stress was related to the crack opening as σ ∝ δ −1/2 .

Cohesive law and notch sensitivity of adhesive joints

A large non-linear zone develops during fracture of a polyurethane adhesive bonded to steel adherends. The fracture process zone was characterised by a traction-separation law, a so-called cohesive law. The cohesive law was determined experimentally by the use of a J integral based approach on double cantilever beam sandwich specimens loaded with pure bending moments. The cohesive law shape was found to be highly non-linear. The cohesive stress increased with increasing separation, reached a peak and then decreased with increasing opening. The effects of loading rate and thickness of the adhesive layer on the cohesive law were investigated. An excellent agreement was found between measured strengths of bonded panels having a central notch and strength predictions based on cohesive law parameters.

Mode I intra-laminar crack growth in composites - modelling of R-curves from measured bridging laws

In this paper R-curves for mode I crack growth in composites are modelled based on measured bridging laws. It is shown that simulated and measured R-curves are in good agreement. Simulations show that variations in the measured bridging law parameters can explain the scatter in overall R-curves. Finite element procedures for treating a generalised nonlinear law for intra-laminar fibre bridging (longitudinal splitting) in combination with R-curve modelling are demonstrated for mode I loading. The difference between calculating the crack growth resistance by linear elastic fracture mechanics and by the J integral for the double cantilever beam specimen loaded by wedge forces is elucidated. It is shown that calculating the crack growth resistance by linear elastic fracture mechanics results in overestimation of the steady-state crack growth resistance.

Effects of nonuniformity of fiber distribution on thermally-induced residual stresses and cracking in ceramic matrix composites

Abstract A three-dimensional finite element analysis is conducted to estimate stresses induced by thermal cooldown in unidirectionally fiber-reinforced ceramic matrix composites. Various configurations of nonuniform fiber distributions are considered. Both cases of thermal expansion mismatch between isotropic, linearly thermoelastic fibers and matrix are studied. Significant effects of nonuniformity of fiber distributions on the local stress states are found. The initiation of various possible cracking modes is discussed in the light of these results.

Controlled crack growth in ceramics : The DCB specimen loaded with pure moments

Abstract The energy release rate of a double cantilever beam (DCB) loaded with pure bending moments is independent of crack length, allowing stable crack growth in even truly brittle materials. The method is thus suitable for measuring fracture toughness and R-curve behaviour of ceramics. This paper describes the development of a new test configuration and reports the testing results from two ceramics: one with constant fracture toughness and one possessing R-curve behaviour due to phase transformation. Stable crack growth was obtained for both materials.

Thermally induced delamination of multilayers

Steady-state delamination of multilayered structures, caused by stresses arising during processing due to thermal expansion mismatch, is analyzed by a fracture mechanics model based on laminate theory. It is found that inserting just a few interlayers with intermediate thermal expansion coefficients may be an effective way of reducing the delamination energy release rate. Uneven layer thicknesses and increasing elastic mismatch are shown to raise the energy release rate. Experimental work confirms important trends of the model.

Crack growth in composites Applicability of R-curves and bridging laws

Abstract Problems arising during characterisation of fracture resistance due to fibre bridging are reviewed and discussed. A distinction is made between small scale bridging and large scale bridging. Simple criteria are used to distinguish between the two types of bridging. Under small scale bridging the crack growth resistance can be characterised by an R-curve. However, under large scale bridging the shape of the R-curve depends on specimen geometry. Therefore, it is preferable to characterise large scale bridging by a bridging law. Methods for determining bridging laws are discussed. Experimental results indicate that the bridging law is independent of specimen geometry, i.e. a material property. Finite element procedures for implementation of bridging laws in component design are outlined.

Measurement of Interface Fracture Toughness of Sandwich Structures under Mixed Mode Loadings

Fracture of sandwich structures loaded with axial forces and bending moments is analyzed in the context of linear elastic fracture mechanics. A closed form expression for the energy release rate of interface cracking of a sandwich specimen is found by analytical evaluation of the J-integral. A method for determining the mode mixity is described and applied. Expressions are presented whereby the mode mixity can be calculated analytically for any load combination when the mode mixity is known for just one load case. The theory presented is applied to a new test method based on double cantilever beam sandwich specimens loaded with uneven bending moments. The interface fracture toughness of two sandwich types are measured as function of the mode mixity. The sandwich structures that are tested consist of glass fiber reinforced polyester skins and PCV core. The tests show that the interface fracture toughness depends strongly on the mode mixity. Under dominated normal crack opening, the crack grows just below the interface in the core at a constant fracture toughness. Under dominated tangential crack deformation, the crack grows into the laminate resulting in extensive fiber bridging and an increase in fracture toughness. As a result of the development of a large process zone due to fiber bridging, the analysis by linear elastic fracture mechanics becomes invalid and modeling with cohesive zones is proposed.

Micromechanical analysis of damage mechanisms in ceramic-matrix composites during mechanical and thermal cycling

Abstract This work presents a micromechanical study of the cyclic response of a undirectionally reinforced ceramic-matrix composite under time-varying load, parallel to fibres, and under thermal cycling. The analysis was based on the finite element method. The overall response was deduced from the response of a representative volume element consisting of concentrically placed cylinders of fibre and surrounding matrix, bounded axially by a matrix crack and a symmetry plane. The interface between the fibre and the matrix was assumed to be a frictional sliding contact (Coulomb friction). The results of this study indicated that the interfacial sliding stress τs may be assumed to be constant over the sliding distance, whereas its variation with the remote applied stress is important. It was also found that the overall stress/strain behaviour is non-linear when the state of interfacial sliding is changing, while a linear response results for a fully sliding interface. In the latter case, the tangential modulus in loading differs from that in unloading. For thermal cycling, the analysis showed that, due to insignificant interfacial sliding, the thermal expansion coefficients in the damaged state are practically the same as in the undamaged state.