Strain Invariant Failure Theory Research Articles

Consistent approach to onset theory

Onset Theory (previously known as Strain Invariant Failure Theory) is a physics-based composite failure criterion attempting to predict failure at the level of constituents rather than for a homogenized ply. Applying Onset Theory correctly requires a number of steps. As a starting point for other researchers, a consistent approach is developed by resolving contradictions found in literature. This includes the micromechanical FEA process used to determine the individual fiber and matrix strains, such as correct choice of representative volume elements (RVEs), the use of transformed RVEs, boundary conditions, and the location of data extraction points. Analytical expressions are provided to determine the full state of strain in a ply, including in-plane and out-of-plane Poisson’s strains and thermally induced mechanical strains. Literature definitions of the critical invariants are discussed, and a trend in critical distortional invariants is observed. Assumptions and limitations of the theory are identified. Finally, a failure envelope is compared to World Wide Failure Exercise test data.

Experimental and Numerical Study on Long-Life and Progressive Damage in Laminates in Open-Hole Compression Tests

The strength theory design accuracy of carbon fiber reinforced plastics (CFRP) composite structures are integral to CFRP composite structures product weights along with production costs. In order to further improve the CFRP composite structure strength theory design accuracy in this paper, it developed an ATM/SIFT analysis method by combining strain invariant failure theory (SIFT) and Accelerated testing methodology (ATM). The developed implementation scheme of ATM/SIFT includes: three parts of accelerating material strength test, component strength main curve characterization, structures life prediction, among which the material life prediction is achieved by using Python code to customize user material subroutines (VUMAT), through secondary development on the ABAQUS platform. Based on the developed ATM/SIFT method, it analyzed the compressive gradual failure mechanism and life of IM600/TDE-85 composite laminated plates open pore structures. Finally, it predicted the long-term static load compression life of IM600/TDE-85 composite laminate open-hole structures by using ATM/SIFT method and compared this prediction results with test results.

A multiscale modelling procedure for predicting failure in composite textiles using an enhancement approach

Composite materials have largely been analysed for failure and structural performance from the perspective of an anisotropic homogeneous material despite their evident hierarchical nature. Although such an assumption does substantially facilitate the analysis procedure in a computationally efficient manner, predictions on the occurrence of failure differ from reality as the failure mechanisms within composite materials are different from a constituent perspective. This paper demonstrates the ability of a multiscale dehomogenisation procedure that provides failure information at different length scales, namely: the macro- (continuum), meso- (textile) and micro-scale (constituent). This is achieved by adopting an enhancement approach performing simple matrix operations to study the strain distribution. The hierarchical dehomogenisation procedure using Strain Invariant Failure Theory is implemented in Abaqus UMAT subroutine and verified using simple sanity checks and a ‘manual’ sub-modelling technique utilising an open hole tension coupon as an example. A comparison of the two modelling techniques indicate the similar failure predictions at the meso and micro levels with the hierarchical approach presented in this paper being far more computationally efficient. The failure analysis procedure presented in this paper is subsequently demonstrated on a composite I-beam component allowing failure in composite structures to be observed from a constituent perspective where fibre and matrix modes of failure can be identified and examined from an engineering point of view.

Computational implementation and experimental validation of a micro-mechanics informed progressive damage Strain Invariant Failure Theory

The current paper deals with the failure modelling in continuously reinforced composite structures taking into account the material's inherent microstructure. The implementation of a constitutive model for transversely isotropic damage in fibre reinforced composites is presented. Damage initiation in the orthotropic linear elastically modelled composite is governed by the Strain Invariant Failure Theory (SIFT), utilising the first strain invariant and the second deviatoric strain invariant for damage initiation. To phenomenologically account for the material's microstructure, the homogenised macro strain is related to the micro strain by means of strain amplification factors determined from prior simulations of Repeating Unit Cells (RUCs) with different fibre arrangements utilising Periodic Boundary Conditions (PBCs). For validation of the numerically implemented model, experimental tests of composite laminates with varying layups are performed. The conducted experiments are simulated utilising the implemented models and the obtained results are validated with the experimental data.

Strain Invariant Failure Theory – Part 1: An extensible framework for predicting the mechanical performance of fibre reinforced polymer composites

Failure prediction for composite materials is still a major area of interest within both the academic literature and the composite industry. This paper presents a modelling and experimental framework which has been developed for the application of Strain Invariant Failure Theory (SIFT), but which can be adapted to other failure prediction methods if required. SIFT is set of physics-based failure criteria developed to predict the onset of irreversible deformation of glassy polymers. The paper provides an overview of the available evidence for SIFT and provides a complete methodology for applying SIFT to predict the onset of failure in a composite component.Fundamental to the method presented is a modular and hierarchical dehomogenisation procedure; allowing for the evaluation of stress and strain state variables within the constituent components of the composite. Due to the constant evolution of composite characterisation techniques, the method presented in this paper is designed to be extensible (i.e. accommodating of new materials and product forms) and modular (i.e. subsections of the method can be easily substituted or refined). Known limitations of the current method are clearly presented and discussed. A companion paper will present validation of the approach for simple uniaxial and biaxial coupon experiments and will discuss how the method can be applied to a range of existing composite characterisation testing standards.

A multiscale progressive damage analysis for laminated composite structures using the parametric HFGMC micromechanics

A nonlinear multiscale damage analysis is proposed based on the parametric High Fidelity Generalized Method of Cells (HFGMC) micromodel. Two repeating unit-cells (RUCs), square and hexagonal, for the composite microstructure are discretized into subcells which represents the fiber and matrix phases. Average traction and displacement continuities, periodicity conditions, and volumetric equilibrium are applied. The proposed modeling approach is implemented as a user material subroutine within displacement-based layered-shell FE models, where each layer can be represented with at least one RUC. The RUC through-thickness stress and stiffness contributions are eliminated in case of a failure. Two failure criteria, in conjunction with compressive strength equation, are applied to determine RUC failure. In the first, the Tsai-Wu failure criterion is used at the RUC level. The second employs the strain invariant failure theory (SIFT) within each subcell, leading to its extinction. The in-situ properties and damage parameters of the RUC are determined by calibration using axial, transverse, and shear data of unnoteched laminates. The accuracy of the proposed framework is demonstrated by a comparison with experimental results of open-hole laminates.

Calculation of strain amplification matrix for strain invariant failure theory based on representative volume element models with periodical boundary condition

Strain invariant failure theory (SIFT) is a micro-mechanics-based failure theory for multi-scale failure analysis of composite materials originally proposed by Gosse and Christensen. In this paper, the approach for obtaining strain amplification matrix which is a key step for the execution of SIFT is improved by adopting representative volume element (RVE) finite element models considering periodical boundary condition, based on which more actual deformation mode is reflected. The deformation modes and strain data at the characteristic points of the centroid cell of multi-cell RVE model are analyzed and taken as a reference. It can be concluded that more reasonable deformation mode and relationship between the micro-mechanical and macro-mechanical strain states are obtained by employing the new model. Finally, numerical examples are provided to illustrate the determination of strain amplification factors within the RVEs considering periodical boundary condition at the characteristic points.

Post-buckling progressive damage of CFRP laminates with a large-sized elliptical cutout subjected to shear loading

Cutouts are always located in aerospace composite structures to meet specified requirements on the service and functions. The presence of cutout, especially large-sized cutout, would result in a significant stress concentration, and consequently a complicated failure mechanism. This paper presents an experimental and numerical study on the post-buckling damage process of high-performance carbon fiber reinforced polymer (CFRP), T800/X850, multidirectional composite laminated specimen. The simply supported specimen is with a central large-sized elliptical cutout and subjected to shearing load. In the numerical analysis, a damage model incorporating both advanced strain softening schemes and cross-coupling effect between the failure mechanisms is constructed for the damage simulation. Regularizations are implemented for coupling the damage variables to address the deficiencies of the existing model and access the real physical damage behavior of laminated composites. The strain invariant failure theory is employed for evaluation of delamination. To assess the objectivity of the present numerical model, the numerical predictions are compared with experimental data. The predicted damage and propagation patterns show good agreement with experiment results.

Prediction of Long-Term Compression Strength for Quasi-Isotropic CFRP Laminates

Long-term strength prediction method is developed based on three theories: accelerated testing methodology (ATM), strain invariant failure theory (SIFT) and progressive damage analysis (PDA). It can predict the strength and damage at a given failure time. Net resin 5228A was experimented by dynamic mechanical analysis and static tensile loading under various temperatures to determine the time-temperature shift factors and master curve of Young’s modulus. Unidirectional laminates of CCF300/5228A were tested under different temperatures to calculate the SIFT/ATM critical parameters. Long-term strength of quasi-isotropic composite laminates (QIL) was predicted. Good agreement between numerical results and experiments is observed, which demonstrates the applicability of this method.

Biaxial Specimen Design for Structures Subjected to Multi-Axial Loads

The ability to optimise structures requires a thorough understanding of the loadsthat they are subjected to. Many composite materials in use today are subjectedto complex loading patterns that exhibit multi-axial stress and straincharacteristics. It is not sufficient to model material data for thesestructures based purely on uniaxial information. Unlike the well understoodfailure criteria of materials when subjected to uniaxial loads; biaxial failureenvelope has not been defined with sufficient experimental data particularly inthe tensile load region. There has not been any standard specimen geometrydefined for biaxial testing. Also the effective area when subjected to loadingis not as easily known as is the case in uniaxial loading. Thus biaxial testspose a greater level of difficulty when establishing failure stresses for thematerial. The authors look at establishing a specimen geometry that is suitablefor use preliminarily in isotropic materials. These specimen geometries must beable to ensure failure at the anticipated gauge region. Investigation into thefirst quadrant of the biaxial failure envelope under tension-tension is lookedat with insight into matrix failure as the dominant mode of failure. Numerical resultsand preliminary experimental results for FM355 epoxy specimens are presentedand compared with existing failure models such as Von Mises criterion and thefailure criterion used in Strain Invariant Failure Theory.

멀티스케일 모델링 기법을 이용한 섬유강화 복합재료의 미시역학적 파손예측 및 검증

In this paper, a micro-mechanical failure prediction program is developed based on SIFT (Strain Invariant Failure Theory) by using the multi-scale modeling method for fiber-reinforced composite materials. And the failure analysis are performed for open-hole composite laminate specimen in order to verify the developed program. First of all, the critical strain invariants are obtained through the tensile tests for three types of specimens. Also, the matrices of strain amplification factors are determined through the finite element analysis for micro-mechanical model, RVE (Representative Volume Element). Finally, the microscopic failure analysis is performed for the open-hole composite laminate specimen model by applying a failure load obtained from tensile test, and the predicted failure indices are evaluated for verification of the developed program.

Non-linear strain invariant failure approach for fibre reinforced composite materials

The strain invariant failure theory (Gosse and Christensen, 2001) is a micromechanics-based failure theory that depends on computation of critical strain invariants for the fibre and matrix phases. In this paper, a novel approach is developed for including the non-linear effects of the matrix through the implementation of the J2 flow theory for the matrix response. The non-linear isotropic hardening is introduced for the analysis of a non-linear matrix in square and hexagonal fibre packaging geometries. The results are presented for a common type of structural composite made from carbon fibres and an epoxy matrix. The proposed approach is used to predict the stress and strain concentration factors in a multi-cell array and shows the necessity of including the non-linear response in the analytical approach in this theory.

Application of the strain invariant failure theory (SIFT) to metals and fiber–polymer composites

The strain invariant failure theory (SIFT) model, developed to predict the onset of irreversible damage of fiber–polymer composite laminates, may be also applied to metals. Indeed, it can be applied to all solid materials. Two initial failure mechanisms are considered – distortion and dilatation. The author's experiences are confined to the structures of transport aircraft; phase changes in metals and self-destruction of laminates during curing are not covered. Doing so would need additional material properties, and probably a different failure theory. SIFT does not cover environmental attack on the interface between fibers and resin; it covers only cohesive failures within the fibers or resin, or within a homogeneous piece of metal. In the SIFT model, each damage mechanism is characterized by its own critical value of a strain invariant. Each mechanism dominates its own portion of the strain domain; there is no interaction between them. Application of SIFT to metals is explained first. Fiber–polymer composites contain two discrete constituents; each material must be characterized independently by its own two invariants. This is why fiber–polymer composites need four invariants whereas metals require only two. There is no such thing as a composite material, only composites of materials. The “composite materials” must not be modeled as homogeneous anisotropic solids because it is then not even possible to differentiate between fiber and matrix failures. The SIFT model uses measured material properties; it does not require that half of them be arbitrarily replaced by unmeasurable properties to fit laminate test data, as so many earlier composite failure criteria have. The biggest difference in using SIFT for metals and fiber-reinforced materials is internal residual thermal and moisture absorption stresses created by the gross dissimilarity in properties between embedded fibers and thermoset resin matrices. These residual stresses consume so much of the strength of unreinforced polymers for typical thermoset resins cured at high temperature, like epoxies, that little strength is available to resist mechanical loads. (Thermoplastic polymers suffer far less in this regard.) The paper explains how SIFT is used via worked examples, which demonstrate the kind of detailed information that SIFT analyses can generate.

Long-term Open-hole Compression Strength of CFRP Laminates based on Strain Invariant Failure Theory

This paper deals with the prediction of long-term strength of CFRP structure components based on the combined method of the strain invariant failure theory (SIFT) developed by Gosse and Christensen and the accelerated testing methodology (ATM) developed by Miyano and Nakada. The time—temperaturedependent master curves of SIFT critical parameters are constructed by tension and compression tests for the longitudinal and transverse directions of unidirectional CFRP under various temperatures based on the time-temperature superposition principle which holds for the viscoelastic modulus of matrix resin. These master curves can be used for predicting the long-term strength of composite structures with multi-directional laminations at any time, temperature. The long-term open-hole compression strength of the quasi-isotropic CFRP laminates is predicted using the master curves of SIFT critical parameters based on SIFT/ATM combined method and structural stress and strain analysis by finite element method. The applicability of SIFT/ATM combined method to predict the long-term strength of CFRP structures is experimentally confirmed.

Experimental testing of BMI laminates with stress concentrations and the evaluation of SIFT to predict failure

An experimental investigation was conducted to determine the failure mechanism of notched-composite laminates subjected to tension, compression and shear. The experimental data were used to assess the applicability of point-failure criteria, i.e., strain invariant, for failure prediction. The assessment was achieved by firstly using the finite element method to determine the stress and strain distribution around stress concentrators representative of those encountered in the manufacturing, assembly and operation of composite structures of modern aerospace vehicles, for instance the sharp notches that may arise from impact events. Strength was then predicted using preliminary strain invariant failure theory (SIFT) analyses. Coupons that represented these features were manufactured and tested. Finally the test results were compared to the SIFT predictions.

A Micro—Macro Approach to Modeling Progressive Damage in Composite Structures

Modeling progressive damage in composite materials and structures poses considerable challenges because damage is, in general, complex and involves multiple modes such as delamination, transverse cracking, fiber breakage, fiber pullout, etc. Clearly, damage in composites can be investigated at different length scales, ranging from the micromechanical to the macromechanical specimen and structural scales. In this article, a simple but novel finite-element-based method for modeling progressive damage in fiber-reinforced composites is presented. The element-failure method (EFM) is based on the simple idea that the nodal forces of an element of a damaged composite material can be modified to reflect the general state of damage and loading. This has an advantage over the usual material property degradation approaches, i.e., because the stiffness matrix of the element is not changed, computational convergence is theoretically guaranteed, resulting in a robust modeling tool. The EFM, when employed with suitable micromechanics-based failure criteria, may be a practical method for mapping damage initiation and propagation in composite structures. In this article, we present a micromechanical analysis for a new failure criterion called the strain invariant failure theory and the application of the EFM in the modeling of open-hole tension specimens. The micromechanical analysis yields a set of amplification factors, which are used to establish a set of micromechanically enhanced strain invariants for the failure criterion. The effects of material properties and volume fraction on the amplification factors are discussed.

Damage Progression in Open-hole Tension Laminates by the SIFT-EFM Approach

Predicting and modeling progressive damage in fiber-reinforced composite structures up to and including final failure is a considerable challenge because damage in composite materials is extremely complex, involving multiple modes, such as delamination, transverse microcracking, fiber breakage, fiber pullout, etc. Indeed, damage in composites should be studied at different length scales, ranging from the micromechanical to the macromechanical specimen and structural scales. The challenge, however, is in finding theories and methodologies that will faithfully reflect the structural effects of damage progression without involving an inordinate amount of detail (and effort) in the model, so that designers and engineers will have practical tools. In this article, a novel finite element-based method for modeling progressive damage in fiber-reinforced composites is presented. The element-failure method (EFM) is based on the simple idea that the nodal forces of an element of a damaged composite material can be modified to reflect the general state of damage and loading. This has an advantage over the usual material property degradation approaches in that because the stiffness matrix of the element is not changed, computational convergence is guaranteed, resulting in a robust modeling method. When employed with a suitable micromechanics-based failure criterion, it may evolve into an engineering tool for mapping damage initiation and propagation in composite structures. Here, we have utilized the micromechanical information contained in a new strain invariant failure theory (SIFT) to guide the nodal force modification scheme to model progressive damage. As an application of the SIFT-EFM approach, we present a rational nodal force modification scheme for the modeling of progressive damage in quasi-isotropic composite laminates with open holes, subjected to remote tensile loads. The proposed nodal force modification scheme assumes loss of load-bearing capability in the direction transverse to the fibers for the case of local transverse microcracking, and assumes total loss of load-bearing capability when both transverse microcracking and fiber rupture occur. The study investigates the effect of stacking or layup sequence and shows that it is important to refine the model in the through-thickness dimension and includes nodal force modification for the out-of-plane component. It reinforces the view that damage propagation in composites is a complex three-dimensional event. When compared with experimental data, the predicted damage maps and final failure loads show correct trends and reasonable agreement.

A new integrated micro–macro approach to damage and fracture of composites

The element-failure method (EFM) is a novel finite element-based method for the modeling of damage, fracture and delamination in fibre-reinforced composite laminates. The nature of damage in composite laminates is generally diffused and complex, characterized by multiple matrix cracks, fibre pullout, fibre breakage and delaminations. It is usually not possible to model or identify crack tips in the conventional fashion of fracture mechanics. The central idea of the EFM, on the other hand, is to model the damaged portions with partially failed elements, whose nodal forces have been modified to take into account the local damage modes. This has the additional benefit of unconditional computational stability compared to other methods such as material property degradation (MPD) models. Here, we present the application of EFM with a recently-proposed failure criterion called the strain invariant failure theory (SIFT) in the prediction of complex damage progression in open-hole tension (OHT) composite laminates, and show that the damage patterns and predicted final failure loads are in very good agreement with experiments.

Micromechanical Characterization Parameters for a New Failure Criterion for Composite Structures

Strain Invariant Failure Theory (SIFT) is a newly-developed failure criterion for composite structures [8, 9]. SIFT comprises two main features, namely micromechanical finite element modification and critical strain invariant parameters. Micromechanical finite element modification is performed to incorporate residual strains between fibers and matrix into homogenized finite element lamina solution. The presence of residual strains takes into account the mechanical and thermal (environmental) effects. Critical strain invariant parameters can be obtained from simple tensile test by carefully observing the occurrence of damage initiation in composite constituent. Strain tensors extracted from experiment are substituted into strain invariant parameters of i J1 (first invariant of strain; i = f, m—fiber, matrix) and i vm ε (equivalent strain or von Mises strain; subscript vm stands for von Mises). As noted in [8, 9], three critical strain invariants were found to be the onset of composite failure for carbon-fiber/epoxy system; they are m J1−cr , f vm−cr ε and m vm−cr ε . Micromechanical characterization parameters aim to provide general insight on the critical state of strains in which damage initiation locus may be determined by using SIFT critical parameters. Micromechanical model was subjected to six different loading conditions (three normal deformations and three shear deformations) and strain tensors (ε1, ε2, ε3, ε12, ε13, ε23) were extracted from finite element analysis. Micromechanical characterization parameters were obtained by normalizing the strain invariants of micromechanics analysis with respect to critical strain invariant. Important issues such as effect of fiber volume fraction and fiber packing arrangement are briefly discussed.

Element-Failure: An Alternative to Material Property Degradation Method for Progressive Damage in Composite Structures

In order to develop more rational design and damage tolerance approaches, there is a need for more accurate, realistic, and practical modeling of damage progression in composite structures at the component level, and not just at the laboratory specimen level. This presents a considerable challenge because experimental and analytical results at the specimen level do not always translate to observations of damage at the component or structural levels. In this article, a simple but novel finite element-based method for modeling progressive damage in fiber-reinforced composites is proposed. The element-failure method (EFM) is based on the idea that the nodal forces of an element of a damaged composite material can be modified to reflect the general state of damage and loading. The EFM, when employed with suitable micromechanics-based failure criteria, may be a practical method for mapping damage initiation and propagation in composite structures. This concept is especially useful because the nature of damage in composite laminates is in general complex and diffused, characterized by multiple matrix cracks, fiber pullout, fiber breakage, and delaminations. It is therefore not practical or even possible to identify and model the multitude of cracks in the fashion of traditional fracture mechanics. Currently, progressive damage in composites is most commonly modeled using material property degradation methods (MPDM). Unfortunately, MPDM often employs rather arbitrary and restrictive degradation schemes that, in some cases may result in computational problems. In contrast, computational convergence and stability is always assured in EFM because the stiffness matrix is never altered. Furthermore, no contact algorithm to prevent nonphysical solutions involving interpenetration of delamination and crack surfaces is necessary, because the failed elements are not removed from the model. It is shown in this article that the EFM is a more general method than the MPDM. A comparison study of damage progression and delamination in a composite laminate subjected to three-point bend using a recently proposed failure criterion called the strain invariant failure theory (SIFT) is presented. The results show that the EFM is able to predict the damage pattern more accurately than the MPDM.