Thermoelastic properties of microcracked composite laminates

International Journal of Damage Mechanics

2005

107

114

A theoretical framework which allows determining the whole set of 2-D thermomechanical constants of a damaged laminate as a function of crack density in different layers is presented. In this approach, closed-form expressions, which contain thermoelastic ply properties, laminate layup, and crack density as the input information are obtained. It is shown that the crack opening displacement (COD) and crack face sliding displacement, normalized with respect to a load variable, are important parameters in these expressions influencing the level of the properties degradation. They are determined in this paper using generalized plain strain FEM analysis results for noninteractive cracks. The strong dependence of the COD on the relative stiffness and thickness of the surrounding layers, found in this study, is described by a power law. The methodology is validated and the possible error introduced by the noninteractive crack assumption is estimated by comparing with the 3-D FEM solution for a cross-ply laminate with two orthogonal systems of ply cracks. Experimental data and comparison with other models are used for further verification.

“…The total number of elements used was 36,000 and for one particular case, it was 80,000. The number of elements in the mesh was varied to find the most Gudmundson et al (1993).…”

Section: Elastic Properties Of Damaged Laminatementioning

confidence: 99%

Constitutive Relationships for Laminates with Ply Cracks in In-plane Loading

Lundmark

International Journal of Damage Mechanics

2005

107

114

“…Unfortunately, numerical analysis of the significance of the coupling was not presented. Gudmundson and Zang (1993), Varna (2013) and Lundmark and Varna (2006) considered damaged laminates with general lay-up and used homogenization technique to derive expressions for stiffness and thermal expansion coefficient tensors. These expressions in an exact form link damaged laminate thermo-elastic properties with crack density and local parameters characterizing crack behavior: the average crack opening and crack face sliding displacements normalized with respect to far-field stress and ply thickness.…”

Section: Introductionmentioning

confidence: 99%

Variational models for shear modulus of symmetric and balanced laminates with cracks in 90-layer

Katerelos

Krasņikovs

International Journal of Solids and Structures

2015

a b s t r a c tThree analytical models with increasing complexity, all based on minimization of complementary energy, are compared in their ability to predict shear modulus reduction of laminates with intralaminar cracks in 90-layer. The very elegant and simple (and the less accurate) model by Hashin assumes linear out-of-plane shear stress distribution across the ply in all layers. The second model assumes exponential shape of these stresses in the constraint layer keeping linear assumption in the cracked layer. The model developed in the present paper accounts for nonlinear out-of-plane shear stress thickness distribution in all layers described by shape functions determined in the procedure of minimization. Increasing the complexity of the model the predicted shear modulus of the damaged laminate increases approaching to value obtained using finite elements (FE). Results show that for laminates with relatively thick cracked layers the stress state description in the cracked layer should be refined whereas for laminates with constraint layer thicker than the cracked layer more accurate stress description in the constraint layer is necessary. More accurate solutions could be derived using the described methodology, but the involved complexity and the numerical routines required for their application diminish their value comparing with direct FE solution.

“…Detailed derivation of the damaged laminate stiffness and thermal expansion coefficients’ expressions can be found in Varna 20 and Gudmundson and Zang. 22 The exact expressions linking the macro- and micro scale properties are as follows where [I] is the identity matrix. The matrix-function [K]k for the k th layer is defined as …”

Section: Appendixmentioning

confidence: 99%

“…An alternative to methods using the average stress change due to cracking is a method based on crack face opening and sliding displacements (COD and CSD) developed in various studies 18–20 and first suggested in Gudmundson and Östlund 21 and Gudmundson and Zang. 22 (Note that assumptions used in the latter two papers might significantly overestimate the damaged laminate compliance change. 23 ) Exact closed-form expressions were presented in Varna 20 linking the in-plane thermoelastic constants of the damaged symmetric laminate to the crack density in a ply multiplied by COD and CSD.…”

Section: Introductionmentioning

confidence: 99%

Effective shear modulus of a damaged ply in laminate stiffness analysis: Determination and validation

Loukil

Journal of Composite Materials

2019

The concept of the “effective stiffness” for plies in laminates containing intralaminar cracks is revisited presenting rather accurate fitting expressions for the effective stiffness dependence on crack density in the ply. In this article, the effective stiffness at certain crack density is back-calculated from the stiffness difference between the undamaged and damaged laminate. Earlier finite element method analysis of laminates with cracked 90-plies showed that the effective longitudinal modulus and Poisson’s ratio of the ply do not change during cracking, whereas the transverse modulus reduction can be described by a simple crack density dependent function. In this article, focus is on the remaining effective constant: in-plane shear modulus. Finite element method parametric analysis shows that the dependence on crack density is exponential and the fitting function is almost independent of geometrical and elastic parameters of the surrounding plies. The above independence justifies using the effective ply stiffness in expressions of the classical laminate theory to predict the intralaminar cracking caused stiffness reduction in laminates with off-axis plies. Results are in a very good agreement with (a) finite element method calculations; (b) experimental data, and (c) with the GLOB-LOC model, which gives a very accurate solution in cases where the crack face opening and sliding displacements are accurately described.