P.P. Camanho

Numerical simulation of mixed-mode progressive delamination in composite materials

A new decohesion element with the capability of dealing with crack propagation under mixed-mode loading is proposed and demonstrated. The element is used at the interface between solid finite elements to model the initiation and non-self-similar growth of delaminations in composite materials. A single relative displacement-based damage parameter is applied in a softening law to track the damage state of the interface and to prevent the restoration of the cohesive state during unloading. The softening law is applied in the three-parameter Benzeggagh-Kenane mode interaction criterion to predict mixed-mode delamination propagation. To demonstrate the accuracy of the predictions, steady-state delamination growth is simulated for quasi-static loading of various single mode and mixed-mode delamination test specimens and the results are compared with experimental data.

Failure criteria for FRP laminates

A new set of six phenomenological failure criteria for fiber-reinforced polymer laminates denoted LaRC03 is described. These criteria can predict matrix and fiber failure accurately, without the curve-fitting parameters. For matrix failure under transverse compression, the angle of the fracture plane is solved by maximizing the Mohr-Coulomb effective stresses. A criterion for fiber kinking is obtained by calculating the fiber misalignment under load and applying the matrix failure criterion in the coordinate frame of the misalignment. Fracture mechanics models of matrix cracks are used to develop a criterion for matrix failure in tension and to calculate the associated in situ strengths. The LaRC03 criteria are applied to a few examples to predict failure load envelopes and to predict the failure mode for each region of the envelope. The analysis results are compared to the predictions using other available failure criteria and with experimental results.

A progressive Damage Model for Mechanically Fastened Joints in Composite Laminates

A three-dimensional finite element model is developed to predict damage progression and strength of mechanically fastened joints in carbon fibre-reinforced plastics that fail in the bearing, tension and shear-out modes. The model is based on a three-dimensional finite element model, on a three-dimensional failure criterion and on a constitutive equation that takes into account the effects of damage on the material elastic properties. This is accomplished using internal state variables that are functions of the type of damage. This formulation is used together with a global failure criterion to predict the ultimate strength of the joint. Experimental results concerning damage progression, joint stiffness and strength are obtained and compared with the predictions. A good agreement between experimental results and numerical predictions is obtained.

Stress analysis and strength prediction of mechanically fastened joints in FRP: a review

A review of the investigations that have been made on the stress and strength analysis of mechanically fastened joints in fibre-reinforced plastics (FRP) is presented. The experimental observations of the effects of joint geometry, ply-orientation, lay-up and through-thickness pressure on the joint behaviour are described briefly for both single and multi-fastener joints. The analytical and numerical methods of stress analysis required before trying to predict failure are discussed. The numerical approaches cover both two and three-dimensional models and the effects of clearance, friction and geometry are assessed. The several methods that have been used to predict failure in single or multi-fastener joints are described. It is concluded that there are some issues that require further investigation. There is no general agreement about the method that should be used to predict failure, but progressive damage models are quite promising since important aspects of the joints behaviour can be modelled using this approach. In order to take into consideration several factors related to joint strength the use of three-dimensional models is suggested. These models require a three-dimensional failure criterion and an appropriate property degradation law.

Failure Criteria for FRP Laminates in Plane Stress

Abstract A new set of six failure criteria for fiber reinforced polymer laminates is described. Derived from Dvorak’s fracture mechanics analyses of cracked plies and from Puck’s action plane concept, the physically-based criteria, denoted LaRC03, predict matrix and fiber failure accurately without requiring curve-fitting parameters. For matrix failure under transverse compression, the fracture plane is calculated by maximizing the Mohr-Coulomb effective stresses. A criterion for fiber kinking is obtained by calculating the fiber misalignment under load, and applying the matrix failure criterion in the coordinate frame of the misalignment. Fracture mechanics models of matrix cracks are used to develop a criterion for matrix in tension and to calculate the associated in-situ strengths. The LaRC03 criteria are applied to a few examples to predict failure load envelopes and to predict the failure mode for each region of the envelope. The analysis results are compared to the predictions using other available failure criteria and with experimental results. Predictions obtained with LaRC03 correlate well with the experimental results.

Mixed-Mode Decohesion Elements for Analyses of Progressive Delamination

A new 8-node decohesion element with mixed mode capability is proposed and demonstrated. The element is used at the interface between solid finite elements to model the initiation and propagation of delamination. A single displacement-based damage parameter is used in a strain softening law to track the damage state of the interface. The method can be used in conjunction with conventional material degradation procedures to account for inplane and intra-laminar damage modes. The accuracy of the predictions is evaluated in single mode delamination tests, in the mixed-mode bending test, and in a structural configuration consisting of the debonding of a stiffener flange from its skin.

Effective simulation of delamination in aeronautical structures using shells and cohesive elements

A cohesive element for shell analysis is presented. The element can be used to simulate the initiation and growth of delaminations between stacked noncoincident layers of shell elements. The procedure to construct the element accounts for the thickness offset by applying the kinematic relations of shell deformation to transform the stiffness and internal force of a zero-thickness cohesive element such that interfacial continuity between the layers is enforced. The procedure is demonstrated by simulating the response and failure of the mixed-mode bending test and a skinstiffener debond specimen. In addition, it is shown that stacks of shell elements can be used to create effective models to predict the in-plane and delamination failure modes of thick components. The results indicate that simple shell models can retain many of the necessary predictive attributes of much more complex three-dimensional models while providing the computational efficiency that is necessary for design.

Failure mechanisms in bolted CFRP

An experimental investigation on the damage mechanisms of mechanically fastened joints in composite laminates is presented. This information concerning damage mechanisms is required before developing damage progression models. For doublelap joints with fingertight washers, specimens that fail in the bearing, tension and shearout modes are investigated. For fully failed specimens and for specimens loaded to several percentages of failure load, the damage mechanisms are investigated using Xradiography and sectioning. It is concluded that failure occurs by a process of damage accumulation, where the failure mechanisms present are fiber fracture, delamination at the laminate loaded hole, matrix cracks and related fiber microbuckling, and internal delamination. Modelling this interaction between failure mechanisms requires further analytical efforts. Due to the importance of the through-thickness stresses present at the hole boundary, delamination has a significant effect on the joint strength, so the use of a threedimensional failure criterion is suggested.

A Three-dimensional Damage Model for Transversely Isotropic Composite Laminates

This article proposes a fully three-dimensional continuum damage model, developed at the sub-ply level, to predict in an integrated way both the intralaminar and the interlaminar failure mechanisms that occur in laminated fiber-reinforced polymer composites. The constitutive model is based on the assumption that the composite material is transversely isotropic, and accounts for the effects of crack closure under load reversal cycles. The damage model is implemented in an implicit finite element code taking into account the requirement to ensure a mesh-independent computation of the dissipated energy. The comparison between the model predictions and published experimental data indicates that the model can accurately predict the effects of transverse matrix cracks on the residual stiffness of quasi-isotropic laminates, the interaction between transverse matrix cracks and delamination, and final failure of the laminate.

A Theoretical Model to Study the Influence of Tow-drop Areas on the Stiffness and Strength of Variable-stiffness Laminates:

Variable-stiffness laminates that have fiber orientation variation across its planform can be manufactured using advanced fiber placement technology. For such laminates, successive passes of the fiber placement head often overlap resulting in thickness build-up. If a constant thickness is desired, tows will be cut at the course boundary, which can result in small triangular resin-rich areas without any fibers. In this article a theoretical, numerical investigation of the influence of these tow-drop areas on the strength and stiffness of variable-stiffness laminates is performed. The effects of tow width, laminate thickness and staggering in combination with tow-drop areas are studied by making use of finite element simulations. A method for the localization of tow-drop areas is presented, and the expressions for implementing the tow-drop areas in a finite element model are given. Subsequently, progressive failure analyses using the LaRC failure criteria are performed. Failure occurs at tow-drop locations in both the surface plies and underlying plies. Wider tows result in lower strength. No correlation seems to exist between thickness and laminate strength, while staggering has a positive influence on strength.