Average Crack Opening Displacement Research Articles

Tensile damage evolution and mechanical behaviour of SiCf/SiC mini-composites through 4D in-situ micro-CT and data-driven modelling

Damage evolution of SiCf/SiC ceramic matrix mini-composites (CMMCs) was characterised by using a 4D in-situ micro-computed tomography (CT) tensile test and digital volume correlation (DVC) technique. Additionally, a CT damage data-driven shear lag model was developed to predict its tensile stress-strain response. A 4D in-situ X-ray CT tensile test of a unidirectional SiCf/SiC mini-composite was first carried out. Then two ad-hoc deep-learning image segmentation models were developed to automatically identify its microstructure and damages induced by tension, respectively. Damage evolution was quantitively characterised by visualising the initiation and propagation of matrix cracks in three-dimensions (3D). A two-step approach was employed to evaluate its 3D internal strain distributions at various loading levels, which further revealed strain concentrations and helped establishing the tensile stress-strain response of the CMMCs. It was observed that transverse cracking is the predominant damage mode, and the average crack opening displacement increases with loading. A high-fidelity X-ray CT data-driven shear lag model was developed, incorporating inputs of transverse matrix crack spacing calculated by the 4D in-situ CT test data. The predicted stress-strain response showed a good correlation with the experimental results.

Crack density-based semi-quantitative estimation for leak rate of composite laminates with thin-plies

To predict the leakage of composite fuel tanks due to matrix cracks, this paper proposes novel simulation schemes: (1) A semi-quantitative leak rate estimation method is developed based on the crack intersection area; (2) The semi-analytical damaged constitutive model is obtained by a small amount of micro-mechanical finite element analysis (FEA); (3) The mixed mode crack density is estimated by using the FEA of laminates, which involves the progressive damaged properties; (4) The crack intersecting area is estimated based on the crack density and the crack opening displacement (COD), which is considered as the product of the average unit COD and the strain component. Two sets of simulations are set at room temperature to validate the method in detail, to verify the mechanics of leakage due to the matrix cracks, and to find out the effect of the thin-plies on the leakage. This paper aims at providing new simulation schemes for damaged constitutive model, crack density prediction and leak rate estimation of the composite laminates.

Thermoelastic constants of symmetric laminates with cracks in 90-layer: application of simple models

The change of thermoelastic properties of cross-ply and quasi-isotropic laminates with intralaminar cracks in layers is analysed. Predictions are performed using previously derived general expressions for stiffness of symmetric damaged laminates as dependent on crack density and crack face opening and sliding. It is shown that the average crack opening displacement can be linked with the average value of axial stress perturbation between two cracks. Using this relationship, analytical shear lag and Hashin’s models, developed for axial modulus, can be applied for calculating thermal expansion coefficients, in-plane moduli and Poisson’s ratios of damaged laminates. The approach is evaluated using finite element method and it is shown that the accuracy is rather similar to that in axial modulus calculation.

Use of full-field measurements to evaluate analytical models for laminates with intralaminar cracks

Full-field displacement measurements between intralaminar cracks in cross-ply laminates were performed to evaluate the accuracy of shear lag models and Hashin’s model. The dependence of the average crack opening displacement on the crack density was measured and compared with model predictions. It was found that Hashin’s model overestimates the average COD by at least 25%. The value of the shear lag parameter was back-calculated by fitting. With the same goal the strain in the middle between two cracks was measured rendering shear lag parameter which was only 1% different. The found value does not agree with any of the used shear lag models. Measurement shows nonzero intralaminar shear zones in both layers covering a part of the ply thickness.

Estimation of mesoscale strain with fatigue crack propagation through quantitative analysis of displacement vector fields by a television-optical measuring complex

In the work, a computational algorithm for crack opening through surface image processing of loaded materials in fatigue fracture was developed and studied in experiment. In the first part of the paper we analyze model displacement fields to test and verify the proposed procedure and software, and in the second part, we consider experimentally taken images of surface regions with a propagating fatigue crack. It is shown that for experimental study of fatigue fracture, it is appropriate to use two parameters: the average crack opening displacement and the shear strain intensity around the crack tip. Analysis of images containing both a deformation zone and an opening crack reveals a nonlinear dependence of the crack opening displacement on the shear strain intensity and this suggests that the computation domain fails to cover the entire strain localization zone.

COD-based simulation of transverse cracking and stiffness reduction in [S/90 n] s laminates

Closed-form expressions for the thermo-elastic properties of [S/90 n ] s laminates with transverse cracks in the 90° layers are derived. Provided the normalised average crack-opening displacement (COD) is known, expressions contain only crack density, geometrical parameters and elastic constants of layers. The average COD dependence on the crack spacing and constraint effect of adjacent sub-laminates is analysed by using finite-element method in plane stress formulation. It is found that the out-of-plane elastic constants have an insignificant effect on COD. A simple power law relating average COD to elastic and geometrical parameters of constituents is derived. The obtained power law and the developed methodology are successfully used to predict the reduction of thermo-elastic properties and damage evolution of [±θ/90 4] s laminates. The crack-closure technique and Monte-Carlo simulations are used to model the damage development. The 90° layer is divided in to a large number of elements and G c values are assigned to each element according to a Weibull distribution. Parameters in the Weibull distribution are determined by using experimental crack density versus strain curve for glass-fibre/epoxy [0 2/90 4] s cross-ply laminates. Damage development in [S/90 4] s laminates of the same material, containing sub-laminates with ±θ layers only, is modelled by using these Weibull parameters and the results are in good agreement with test data. The effect of the thickness of the 90° layer on damage development is discussed in strength and fracture mechanics formulation.

Mixed Micromechanics and Continuum Damage Mechanics Approach to Transverse Cracking in [S, 90 n] s Laminates

The stiffness reduction in [S, 90 n ] s laminates due to transverse cracking in 90-layers is analyzed using the synergistic continuum damage mechanics (SCDM) and a micromechanics approach. The material constants involved in the SCDM model are determined using the stiffness reduction data for a reference cross-ply laminate. The constraint efficiency factor, which depends on the stiffness and geometry of neighboring layers, is assumed to be proportional to the average crack opening displacement (COD). The COD as a function of the constraint effect of adjacent layers and crack spacing is described by a simple power law. The crack closure technique and Monte Carlo simulations are used to model the damage evolution: the 90-layer is divided into a large number of elements and the critical strain energy rate G c having the Weibull distribution is randomly assigned to each element. The crack density data for a [02/904] s cross-ply laminate are used to determine the Weibull parameters. The simulated crack density curves are combined with the CDM stiffness reduction predictions to obtain the stiffness versus strain. The methodology developed is successfully used to predict the stiffness reduction as a function of crack density in [±θ/904] s laminates.

Analytical modeling of stiffness reduction in symmetric and balanced laminates due to cracks in 90° layers

Stiffness reduction in [S,90 n] s symmetric laminates, containing orthotropic sub-laminates ( S) and cracked 90° layer, is analyzed. Closed-form expressions relating stiffness changes to the transverse crack density are derived. They contain only material properties, laminate geometry and a stress-perturbation function that is proportional to the normalized average crack-opening displacement. Stress-distribution models [shear lag, based on variational approach, and finite-element analysis (FEA)] are adopted for the [S,90 n] s configurations and used to calculate the stress-perturbation function. Predictions are compared with experimental data for [ θ, 90 4] s θ=0, 15, 30, 40 glass-fiber/epoxy-resin laminates. Generally the FEA model slightly underestimates stiffness reduction whereas both of the variational models used lead to similar results, slightly lower than experimental. Even the shear-lag model may be successfully used if the shear-lag parameter is first obtained from fitting test results for cross-ply laminate of the same material.

Transverse cracks in cross-ply laminates 2. Stiffness degradation

From the results of stress analysis between two transverse cracks in cross-ply laminate [1], a model for the stiffness reduction based on generalized plane strain assumptions has been developed. Simple analytical expressions are obtained for the longitudinal modulus and the Poisson's ratio as a function of the transverse crack density. Apart from the crack density, these expressions depend only on the elastic and geometrical properties of constituent laminae and the average crack opening displacement (ACOD) normalized in the proper way. Calculations of the ACOD are performed and analyzed with the FEM and analytical models used for the stress analysis in [1]. The predicting capabilities of approximate models are discussed in comparison with experimental data and FEM results. In order to predict the stiffness degradation for a wide variety of laminates, a simple procedure requiring only one FEM calculation for some “average laminate” with “average crack spacing” is proposed and has been proved effective.

複合材料積層板におけるトランスバースクラックの損傷力学解析

Damage mechanics is applied to the prediction of transverse cracking in composite laminates. The analysis is performed by assuming that the average crack opening displacement of a transverse crack can be approximated by that in an infinite homogeneous transversely isotropic medium. The analysis elucidates the thermomechanical properties of the laminates with transverse cracks and gives the energy release rate associated with transverse cracking. By assuming that a transverse crack occurs when the energy release rate reaches a critical value and by incorporating the thermal residual stresses arising from the mismatch of thermal expansion coefficients between plies, the transverse crack density is predicted as a function of the laminate stress. The prediction is compared with the experimental results of CFRP cross-ply (0/90m/0) (m=4, 8 and 12) laminates. An advantage of the present analysis is that it can be applied to an arbitrary laminate.

A theory for the diffraction of SH waves by randomly rough surfaces in two dimensions

In this paper we shall consider a mathematical model for the diffraction of SH waves by randomly rough surfaces. We use the crack Green function method to formulate the problem (see G. R. Wickham, Proc. R. Soc. A 378 (1981) 241-261, P. A. Lewis and G. R. Wickham, Phil. Trans. R. Soc. A 340 (1992) 503-529). This method gives rise to a Fredholm integral equation of the second kind for the jump in in the potential across the scatterer (also known as the crack opening displacement). To analyse the expectation of the crack opening displacement we use a smoothing method in which we perform an ensemble average over all realizations of a certain class of surfaces. A closure assumption is made which is valid for surfaces with small root mean square height. This gives rise to a coupled system of Fredholm integral equations for the average of the crack opening displacement and the average of the random components of the crack opening displacement and kernel. If we make the further assumption that the root mean square gradients are also small, then this coupled system reduces to a single Fredholm integral of the second kind for the expectation of the crack opening displacement. Numerical results are presented for the average crack opening displacement and the average scattered field.

A Study of the Opening Displacement of Transverse Cracks in Cross-Ply Laminates

Transverse cracks in cross-ply laminates are investigated experimentally to reveal the essential characteristics of their opening displacement under tensile loads. The average crack opening displacement is studied as a function of the longitudinal overall strain and the effects of matrix toughness and transverse ply thickness on this parameter are examined. The interactive effects between closely spaced transverse cracks are also ex amined and found to be significant. Implications of the experimentally observed features on the micromechanics and continuum damage type models are discussed.