Tsai-Wu Criterion Research Articles

A novel continuum damage evolution model based on the concept of damage driving force for unidirectional composites

A novel damage evolution model for unidirectional (UD) composites is established in this paper in the context of continuum damage mechanics (CDM). It addresses matrix cracking and it is to be applied along with the damage representation established previously. The concept of damage driving force is employed based on the Helmholtz free energy. It is shown that the damage driving force can be partitioned into three parts, resembling closely three conventional modes of fracture, respectively. A damage evolution law is derived accordingly based on the newly obtained expressions of the damage driving force. The fully rationalised Tsai-Wu criterion is employed in the model for predicting the initiation of matrix cracking damage and fibre failure, assisted with the rationalised maximum stress criterion for identifying the damage modes. A mechanism is introduced to describe the unloading behaviour as a part of the proposed model. The predictions were validated against experimental results, showing good agreement with the experiments and demonstrating the capability and effectiveness of the proposed model.

Examining the effect of the shear coefficient on the prediction of progressive failure of fiber-reinforced composites

The ultimate damage of composites under tension usually results from fiber damage, which includes both tensile and shear contributions. In this study, the shear coefficient α of the fiber yarn is incorporated into the failure criterion to consider the shear effect of the fiber yarn. An analytical model is then proposed that combines a homogenization method and the enhanced failure criterion to facilitate quick evaluation of the progressive damage and failure of the composite. The sensitivity of α on the behaviors of progressive damage and failure are comprehensively explored for different types of fiber-reinforced composites, including a laminate, a plain weave composite, a two-dimensional triaxially braided composite, and a three-dimensional woven composite. The results indicate that damage and failure behaviors are generally sensitive to the shear coefficient, and composites with more complex textile structure demonstrates greater sensitivity to the α. An analysis of the sensitivity of α for different failure criteria was also conducted, and the results reveal that the Hashin–Hou criterion shows more sensitivity to α than the Chang–Chang criterion, the Hoffman criterion, or the Tsai–Wu criterion. Therefore, the identification of the shear coefficient is significant for exploring the damage and failure behaviors of fiber-reinforced composites.

Predictive analysis of tensile strength ratios in laminated bamboo composites: Unraveling the stochastic impact of ply angle variations through machine learning model

Laminated bamboo composites (LBC), made by sandwiching bamboo strips, offer promising alternatives to traditional construction materials, especially for housing. However, subjection to the continuous static loading makes these materials initiate cracks inside their various ply. This study uses classical laminate theory (CLT) to determine the strength ratio (SR) of the LBC at different ply orientations by applying Tsai-Wu and Tsai-Hill failure criteria using MATLAB. The study aims to calculate the SRs for LBCs using CLT, employing an ANN model and stochastic finite element (FE) modeling to investigate SRs of five-layered LBCs with varying ply orientations. Applying CLT, the highest SR was determined to be 1.5375 × 107 N/m for the [0°/0°/0°/0°/0°] laminate, as per both failure theories. The study reveals substantial SR variations depending on ply orientation, consistently showing higher SR predictions with the Tsai-Wu theory compared to the Tsai-Hill theory. Next, the study emphasizes the deterministic methodologies to account for the stochastic effects of ply angle on the obtained SR of LBCs. Monte Carlo simulation (MCS) was utilized to model 10,000 randomly generated ply angle inputs and their associated SRs. By incorporating MCS to introduce ±1% variations in ply angles and utilizing normally distributed data, this research effectively captures uncertainties associated with ply orientation. Finally, to forecast the random SR of LBC with various ply orientations, an artificial neural network (ANN) surrogate model is employed. The stochastic analysis confirms the need to quantify the associated uncertainties. The findings of this study are crucial for advancing the application of LBC in sustainable construction, providing valuable insights into their mechanical behavior under different ply orientations, considering the stochastic effect in properties.

Interaction of multiple micro-defects on the strength and failure mechanism of UD composites by computational micromechanics

The mechanical properties of unidirectional fiber-reinforced plastic (UD-FRP) are affected by a variety of micro-defects, such as random fiber arrangement, fiber misalignment and micro-voids. This study aims to investigate how these multiple micro-defects interact with each other and how they affect the strength and failure mechanism of UD-FRP by means of computational micromechanics. The composite behavior was simulated by the finite element analysis of a representative volume element of the composite microstructure in which the random distribution of fibers, the micro-voids, and the fiber misalignment are explicitly included. Both matrix and interface failure were considered for the loadings of transverse tension/compression, longitudinal compression, transverse/longitudinal shear, and their combination. It was found that these three micro-defects significantly weakened the compressive strength of UD-FRP along the longitudinal direction. Especially, the fiber misalignment magnified the effect of fiber arrangement, while the micro-voids reduce the effect. Besides, the fiber arrangement and micro-voids significantly weakened the tensile and compressive strength of UD-FRP along the transverse direction, but their interaction effect was not obvious. Moreover, transverse and longitudinal shear strength are significantly affected by micro-voids, but only longitudinal shear is affected by geometric fiber arrangement, and this effect is also weakened by micro-voids. Finally, the damage envelope under the combined longitudinal compression and transverse loads was obtained and compared with the Tsai-Wu failure criterion. The results showed that the Tsai-Wu criteria can provide an effective estimation for the failure locus under this biaxial loading condition.

Validation of the fully rationalized Tsai-Wu failure criterion for unidirectional laminates under multiaxial stress states through a ring-on-ring test

Validating a failure criterion under complex stress states is important because composites often encounter multiaxial stress in practical applications, but it also helps to expose any deficiencies of the criterion in failure prediction in the presence of stress interactions. This study examines the recently formulated fully rationalized Tsai-Wu criterion for unidirectional laminates under multiaxial stress states created by ring-on-ring loading. Distinct stress distributions under this loading condition are exhibited and quantified by numerical modeling, featuring critical biaxial tension on the bottom surface and triaxial compression on the top surface. The fully rationalized Tsai-Wu criterion and the original Tsai-Wu criterion are used to predict failure, with the results indicating good agreement between the former and experimental data. In comparison with the latter, quadric failure surfaces of the two criteria are constructed to analyze differences in prediction. The findings demonstrate the validity of the rationalization work for the Tsai-Wu criterion and its potential in predicting failure under multiaxial stress states.

Structural Analysis of Deck Reinforcement on Composite Yacht for Crane Installation

The crane installation on the deck of a yacht redistributes the stress field and affects the local structural integrity and performance. The safe operation of the yacht is associated with the optimal placement of the crane on the deck and the proper local structural reinforcement. Here, the structural analysis of the bow part of a yacht made of composite materials is studied, considering the retrofit installation of a crane, in three different cases of reinforcing the deck: (a) without any reinforcement, (b) with a T-type reinforcement, and finally, (c) with a longitudinal beam. The T-type connects the longitudinal bulkhead and the deck, reinforced locally with overlamination skin and adhesive-filler. The longitudinal beam works as a local longitudinal stiffener attached to the deck and connects the second, third, and fourth transverse frames. The structural analysis is performed using the finite element method following the classification societies’ rules. The local reinforcements are made from the same composite materials as the unreinforced deck. The maximum deformations, the principal stresses, and the safety factors following Tsai-Wu and Hashin criteria are calculated and compared for the three different cases. The T-type and longitudinal reinforcements reduce deck stresses by 33%, with longitudinal reinforcement reducing deck deformation by 17%. Composite failure analysis shows the structure was near failure, and the reinforcements enhance safety; T-type is better for multiaxial loads (Tsai-Wu), and longitudinal is superior for micromechanical failure (Hashin). By considering the structural performance and safety aspects, designers and engineers can make optimal decisions regarding yacht crane installation and proper reinforcement, leading to safer and more efficient structures.

The effect of the stress equilibrium factor on the composite case of the solid rocket motor

In this paper, based on the composite structure design and analysis software ANSYS ACP, the layup design for the composite cases of the equal pole hole solid rocket motor with different stress equilibrium factors is carried out. The finite element software ANSYS Workbench is used to study in detail the effects of stress equilibrium factor on the stress level, failure degree, and burst pressure prediction of the case under a certain internal pressure. The results show that reducing the value of the stress equilibrium factor can reduce the stress level of each winding layer along the main direction of the material in the motor case and gradually transfer the maximum stress of the case along the fiber direction from the weak stress zone to the cylinder section. This is beneficial for improving the burst pressure of the case and making the burst point located in the cylinder section. However, whether the case failure is related to the selected failure theory and strength criterion, the failure results and burst pressure obtained using different failure theories and strength criteria may be different, which indicates that each failure criterion has its scope of application and limitations. Under the Tsai-Wu criterion, using the stress equilibrium equation to calculate the stress equilibrium factor can just ensure that each winding layer of the motor case does not fail under the working pressure. In summary, when designing a composite case and predicting its failure, in addition to considering whether the stress equilibrium factor taken is conducive to meeting the design requirements for the strength of the case, it is also necessary to consider the use of multiple failure criteria to study the failure of the case. Obviously, arbitrarily selecting the stress equilibrium factor is not appropriate in the above process. By analyzing the influence of the stress equilibrium factor on the strength and failure condition of the motor case, it can provide an effective reference for the design of a composite case for SRM.

Omni first-ply-failure envelopes — A conservative approach to assess laminate failure

Omni first-ply-failure (FPF) envelopes are an elegant yet conservative approach to assess composite laminate failure on a global level. Omni envelopes can be found increasingly in recent publications. However, the development process of those envelopes shows a lack of clarity. At some point the illustration switches from a laminate-strain basis (ɛx,ɛy,γxy) to the particular case of laminate principal-strain (ɛI,ɛII) basis. The latter is elegant, as the principal-strain space can be easily plotted in 2D. This article presents two procedures to directly determine omni FPF envelopes and it clarifies the transfer to principal strains.While the Tsai–Wu criterion is used in almost all available publications, the present article uses Cuntze’s failure mode concept (FMC). The article provides a simple example case, which demonstrates the application of omni envelopes in context of FEA based CFRP design.

Tensile assessment of woven CFRP using finite element method: A benchmarking and preliminary study for thin-walled structure application

Abstract Carbon-fiber-reinforced polymers (CFRPs) are a composite material popular for thin-walled structure applications because of their advantages over other materials. In this study, numerical simulation analysis based on the finite-element method to identify the tensile behavior of CFRP woven material has been carried out. The method used has been verified and validated using a benchmarking procedure with the results of previous research. Errors in the simulation results are less than 10%, indicating a valid method that can be used for further research. The stress–strain distribution of each layer, the effect of ply orientation on tensile strength, the comparison of failure criteria used, and the comparison of several types of reinforcements often used have been investigated. The results showed that the characteristics of each inner layer received tensile loading visualized in the form of stress strains. Choosing the right layer angle on CFRP woven can affect the performance and strength of the material. Failure criteria that are appropriate to specific application conditions are important. Puck criteria can be used for simple applications, which require only the analysis of the main stresses in the material. Tsai–Hill and Tsai–Wu criteria can provide more accurate predictions and are better suited for loading conditions and more complex material types. Carbon fiber has better characteristics when compared to S-glass and E-glass.

Reliability and sensitivity analyses of porous functionally graded graphene platelet reinforced composite plate

The performance of composite is seriously influenced by numerous uncertain factors, in which the uncertainty analysis plays a vital role in composite materials analysis by providing a comprehensive understanding of uncertain factors and their influence on design and performance. In this study, uncertain behaviors of porous functionally graded graphene platelets reinforced composite (FG-GPLRC) plates are first investigated for assessing the safety under bending deformation. The mechanical model for static analysis of the porous FG-GPLRC plate is formulated by Reddy’s higher-order shear deformation theory, and the bending responses are derived by Hamilton’s principle and the Navier method. Material properties and loads are deemed as random variables, and the performance function is determined by the Tsai-Wu criterion. The univariate dimension reduction method and maximum entropy method are employed to estimate the reliability of porous FG-GPLRC plates with diverse distribution patterns. Additionally, the analytical sensitivities of failure probability with respect to material parameters are derived. The analysis results illustrate that the existence of uncertain factors significantly influences the performance and reliability of composites, and the structural reliability can be improved by adding appropriate pores and graphene platelets at the edge layer of the composite plate.

Experimental Investigation of Mechanical Properties and Failure Mechanisms in Jute-Polyester Composite Laminates under Off-Axis Tensile Loading

Abstract This study focuses on the experimental investigation of the mechanical properties and failure mechanisms of jute-polyester composite laminates under off-axis tensile loading. Various off-axis tests were conducted to analyze the effects of different fiber orientations (0°, 15°, 30°, 45°, 60°, 75°, and 90°) with respect to the load direction. The experimental results revealed a decrease in both off-axis strength and elastic moduli as the off-axis angle increased. Notably, the 45° off-axis tests exhibited the lowest tensile strength and modulus, indicating a more ductile behavior with the highest failure strain. The tensile stress-strain relationship exhibited a nonlinear behavior during off-axis tension loading. Failure analysis was performed using the Tsai-Wu criteria, considering various values of the interaction coefficient F12. The tensile strength and modulus predicted by the Tsai-Wu criteria demonstrated a good correlation with the experimental results. Consequently, the Tsai-Wu criterion proves effective for analyzing the failure properties of woven fabric composites under multiaxial stress conditions.

Composite Plate Optimization: Integrating Analysis Techniques and Design Iterations for Enhanced Mechanical Performance

This essay delves into the comprehensive analysis of composite plate behavior under various loading conditions, focusing on uniaxial loading and the effects of layup design on safety factors. Through a comparative study between Classical Laminate Plate Theory (CLPT) calculations and Finite Element (FE) analysis, discrepancies in stress and strain predictions are identified, attributing them to assumptions made in each method. Furthermore, the essay explores failure prediction using Tsai-Wu criteria and Maximum Stress theory, determining the safety of laminates under different loading scenarios. Additionally, Finite Element analysis is employed to assess the impact of layup design variations on safety factors, leading to recommendations for optimized designs. The limitations of FE models compared to physical tests are discussed, along with alternative approaches such as advanced manufacturing techniques and novel fiber architectures to further enhance safety factors and alter failure modes.

Material Behavior of PIR Rigid Foam in Sandwich Panels: Studies beyond Construction Industry Standard.

A deep understanding of the material parameters and the behavior of sandwich panels, which are used in the construction industry as roof and façade cladding, is important for the design of these construction components. Due to the constant changes in the polyurethane (PU) foams used as a core material, the experimental database for the current foams is small. Nowadays, there is an increasing number of failures of façade and roof panels after installation. This article presents a variety of experimental investigations on sandwich panels from two manufacturers with a core of polyisocyanurate (PIR) rigid foam (density: 40 kg/m3). As part of this study, compression, tension, shear, and bending tests were performed in several spatial directions and over the range required by the standard. The results of the tests showed the orthotropy of the core material and the dependence of the material on the direction and type of load. The stress-strain curves showed linear and non-linear areas. Using the data from this experimental study, a numerical model was implemented which utilized the Hill yield criterion to represent the orthotropy of the core material. The present investigation suggests that the classical von Mises failure criterion, used in many studies, is not suitable for the foam system applied in these sandwich panels. Instead, the Tsai-Wu criterion is more appropriate for defining the failure stresses.

Comparison of different failure criteria in numerical modeling of electron beam cured polymer nanocomposites

In recent times, fibre reinforced polymer (FRP) composites have overtaken the huge market in the world replacing the old conventional materials due to its significant properties. The experimental work conducted to gather the mechanical properties takes alot of time as FRP composites comprises of various geometrical parameters. Therefore, to reduce the experimental encumbrance, the current work is focused on the numerical analysis using different failure criteria, to examine the bearing response of electron beam cured carbon fibre/epoxy (CF/E) composites joint and to get a suitable numerical model. In order to identify the failure of carbon-fibre/polymer composites joints, this work coupled progressive damage analysis (PDA) with the most appropriate failure criteria, namely the Hashin, Tsai-Wu and Maximum stress criteria. Results show that Hashin criterion gave the best suited bearing response predictions. Hashin criterion predicted the maximum bearing capacity in pristine joint specimens, in between 11 and 17% for greater values of W/D and E/D ratios. In multiwalled carbon nanotubes (MWCNTs) added joint specimens, the predicted values by Hashin criterion is in between 14 and 20%.

Prediction Ability Analysis of Phenomenological Strength Criteria for Composites

The article examines and assesses the phenomenological strength theory of composite materials. A comparative analysis of the theoretical envelopes was conducted for each criterion. A unified form of the phenomenological strength criterion was established. The study specifically examined the effects of altering the interaction parameter on the Tsai-Wu criterion’s theoretical envelope. Based on the available experimental data, the study plotted the failure envelopes of each strength criterion under planar composite stress states. The variation of these envelopes across various stress quadrants was highlighted. As a result of the examinations, four typical phenomenological strength criteria were chosen. The composites’ off-axis tensile and biaxial loading test data were used to evaluate the predictive power objectively. The results showed that not all stress states’ test results agreed with the predictions of the phenomenological strength theory. The criterion proposed by Norris and Tsai-Hill performed better at accounting for the material’s different compressive and tensile characteristics. The other criteria tended to be conservative under particular circumstances. Simultaneously, the Hoffman criterion matched the test data more closely over a broader range of stress states. Overall, this study clarified the limitations and applicability of various strength criteria in composite material strength prediction.

Mechanism-Based damage and failure of Fused Filament Fabrication components

Fused Filament Fabrication (FFF) is a polymer-based Additive Manufacturing (AM) technology that produces complex layered components. The characterization of the inherited orthotropic properties of FFF components and their failure analysis is a challenging endeavor. In this paper, the failure mechanics of FFF parts are studied via a Mechanism-Based (MB) damage material model. A MB damage criterion is developed by considering that the damage is driven by different failure modes identified according to the printing pattern. The developed criterion is compared to the Tsai–Wu (TW) criterion, which is commonly used for orthotropic materials with different strengths in tension and compression. Also, a MB cracking model that incorporates the orthotropic brittleness of FFF components is developed. The application of this cracking model requires solely two parameters to be defined.Numerical predictions of the cracking of two different experimental tests illustrate the similarities and the differences between the MB and TW damage criteria. The results demonstrate that the MB damage criterion can accurately match the experimental results, while the TW criterion fails to describe correctly the failure modes in complex 3D stress states.

Orthotropic damage model for composite structures using the 3D Tsai-Wu failure criterion

This paper presents a novel approach concerning the development of an orthotropic damage model based on the original 3D Tsai-Wu failure criterion. In its original formulation, the Tsai-Wu criterion is only capable of identifying the existence of damage at a certain point in the material. However, it is not capable of identifying if the damage is located in the fiber, matrix or interlaminar zone. This work plans to fill this gap in knowledge by providing a simple method, based on equivalent stresses and strains, that identifies the failure modes when the Tsai-Wu failure criterion is near the on-set of damage. Using this novel method, it is possible to implement classical damage evolution laws based on the formulation of Matzenmiller. The proposed damage model is implemented in the commercial finite element software ABAQUS using user-subroutine UMAT, and the numerical results are compared with experimental data obtained earlier by other authors for different applications of glass fiber reinforced polymer (GFRP) structures. The numerical stabilization is achieved by using a new implicit to explicit material time step algorithm.

Numerical generation of omnistrain failure envelopes

Traditional failure criteria for composites are usually formulated in material coordinates and depend on all three inplane stresses, hence failure evaluation depends on the ply angle. The omnistrain failure envelope describes the most critical failure envelope in strain space irrespective of ply orientation. This independence of ply orientation leads to an isotropic failure criterion that depends only on the principal strains. Omnistrain envelopes greatly simplify the task of design and optimisation of composite laminates. This paper proposes a numerical technique to generate omnistrain failure envelopes for different composite failure criteria. The failure index, describing how far a point in strain space is from the failure boundary, is used to describe the failure surface. Assuming convexity of the failure surface, a set of points is generated on the surface, and the convex hull algorithm is used to generate a polygonal approximation of the failure surface. Representing strains in terms of principal strains and the angle between the principal and material coordinates, allows us to eliminate the angle analytically by considering the worst case condition. The omnistrain envelope is thus directly generated from the approximate three-dimensional failure surface. The proposed algorithm does not require analytic expressions of the failure surface. An adaptive algorithm is proposed to generate the omnistrain envelope with relatively small number of points. As demonstration of the proposed algorithm, the omnistrain envelopes for various composite materials are generated for a number of composite failure criteria. The omnistrain envelopes generated for the Tsai-Wu criteria accurately match to existing analytic expressions.

Failure-Averse Active Learning for Physics-Constrained Systems

Active learning is a subfield of machine learning that is devised for design and modeling of systems with highly expensive sampling costs. Industrial and engineering systems are generally subject to physics constraints that may induce fatal failures when they are violated, while such constraints are frequently underestimated in active learning. In this paper, we develop a novel active learning method that avoids failures considering implicit physics constraints that govern the system. The proposed approach is driven by two tasks: the safe variance reduction explores the safe region to reduce the variance of the target model, and the safe region expansion aims to extend the explorable region exploiting the probabilistic model of constraints. The global acquisition function is devised to judiciously optimize acquisition functions of two tasks, and its theoretical properties are provided. The proposed method is applied to the composite fuselage assembly process with consideration of material failure using the Tsai-wu criterion, and it is able to achieve zero-failure without the knowledge of explicit failure regions.

Prediction of the stress distributions and strength properties of 3-D braided composites with an eccentric circular hole

Due to their low delaminating tendency and high damage tolerance, 3-D braided composites are capable of being utilized in notched components. However, a few studies have investigated the mechanical properties of braided composites with open holes in multi-scale. In this paper, a multi-scale study on the mechanical properties of 3-D 4-directional braided composites with an eccentric circular hole is carried out. The equivalent elastic properties of 3-D 4-directional braided composites are calculated by the homogenization method based on the geometry of the meso unit cells. According to Lekhnitskii's theory, the local stress correction (LSC) method for computing the transverse stress around the eccentric hole is proposed. The models of meso unit cells with different braided angles are established, and the strength of the defect-free composites is predicted by the Tsai-Wu criterion. In the macroscopic view, using the point stress criterion (PSC), the average stress criterion (ASC), and numerical analysis, the strength properties of braided composites with different hole radii, braided angles, and eccentric distances are predicted. This study can be utilized to estimate the stress distributions and strength properties of 3-D braided composites with an eccentric hole and provides theoretical and simulation foundations for the problems of orthotropic materials with holes.