A variational method for analysis of laminates with parallel arrays of intralaminar cracks

Abstract

This paper presents a robust variational method for prediction of the effective thermoelastic properties of laminates with parallel, but not necessarily coplanar intralaminar cracks. Arbitrary laminate layup, crack patterns, and any in-plane forces and bending moments, and temperature change can be treated simultaneously. The method is based on the principle of minimum complementary energy. The admissible in-plane stress components are assumed to be linear through the ply thickness. Simple matrix expressions are derived for the effective compliance matrix, thermal expansions and curvatures, and specific heat of a cracked laminate. Predictions for the Young's modulus, Poisson's ratio, shear modulus, flexural rigidity, and thermal expansion as functions of crack density for various laminates of symmetric and nonsymmetric layups demonstrated excellent agreement with experimental results of seven independently published studies. Accuracy and robustness of the method are complemented by the fact that no experimentally fitted parameters are required. It is shown that the same formalism can be applied to analysis of closed intralaminar cracks, as well as nonuniform and nonsymmetrical distributions of cracks.

Measurement of residual strains as a parameter of matrix cracking in CFRP laminates

“…A variational analysis to predict the residual strains existing in the laminates due to the changing of temperature from curing temperature to testing temperature and residual strains due to the matrix cracking are explained in this section. The residual strains can be expressed using the changes of CTE of the laminates when the decrease of CTE due to matrix cracks can be calculated based on the same solution of the energy minimization problem as explained in detail in Vinogradov (2019). The method is based on the principle of minimum complementary energy when the admissible inplane stress components are assumed to be linear through the ply thickness.…”

“…where ( 0 ) is a matrix described in Vinogradov (2019) following from minimization of the complementary energy. Comparing Eq.…”

“…Ogihara and Takeda (1995) for instance, investigated the stiffness reduction by measuring the transverse crack density and delamination ratio in cross-ply laminates where the experimental results were found to be in good agreement to their shear-lag analysis predictions. Recently, Fikry et al (2018) compared their experiment stiffness reduction's result with the variational analysis presented in Vinogradov (2019) for laminates with several off-axis angles where the results were also in a good agreement. Besides that, the Poisson's ratio reduction has also been a subject of investigation, e.g.…”

Damage behaviors in cross-ply cloth CFRP laminates cured at different temperatures

“…We present only a representative result of a specimen as we found that there were almost no variations compared to the other two specimens. The experimental results were compared to the variational analysis results based on the analysis by Vinogradov (2019). In this relationship, crack density is the average number of cracks in a specified measuring area on the laminates while stiffness reduction is the stiffness's reduced rate of perturbated laminates compared to the virgin laminates.…”

“…There are also some studies conducted to investigate the matrix cracks behavior in interlaminar-toughened composite laminates like had been done by Ogihara et al (1998) where the stress and displacement fields in interlaminar-toughened composite laminates with transverse cracks was analyzed. Recently, Fikry et al (2018) experimentally conducted a study on the effects of matrix cracks on the mechanical properties of cross-ply and angle-ply laminates manufactured by prepreg-type fibers which provides validation to the variational analysis results in Vinogradov (2019). They then developed their study about the matrix cracks by experimentally measuring the strain distributions of the cracked laminates using Digital Image Correlation (DIC) and found that secondary mode damages such as oblique and curved cracks have also occurred in the laminates, especially cross-ply laminates with a thick 90degree ply (Fikry et al, 2019).…”