Hashin Criterion Research Articles

Drop Tests and Numerical Analyses of Composite Beams with Corrugated Web

To evaluate the energy absorption ability of composite beams with corrugated web under impact, the drop tests were conducted to demonstrate the fracture modes and obtain the load and energy history curves. Based on the drop tests, a finite element (FE) model was proposed with a weak link designed to trigger crushing, developed using Abaqus/Explicit, which integrates cohesive elements and employs the improved Hashin criterion along with the Choi–Chang criterion to accurately predict the onset and progression of delamination. The model accounts for the anisotropy and progressive damage in composite laminates. The periodic boundary conditions (PBCs) were integrated into the single-wave corrugated web beam model, the inherent limitations of which were corrected, enabling it to simulate the crushing process with the same effectiveness as the multi-wave model. As a result, the proposed model can accurately depict the progressive crushing behavior of corrugated web beams under impact loads while maintaining high computational efficiency.

Assessment of damage prediction models for composite laminates under single and repeated low-velocity impacts

The aim is to explore the influence of damage initiation criteria and evolution methods on the damage prediction for composite laminates under single and repeated low-velocity impacts. A 3D finite element model is established to analyze the impact behavior of laminate, and a damage analysis process including the initiation determination, progressive evolution, and constitutive relationship is designed. Hashin criterion based on tensile strain for matrix is modified by an empirical assumption method. Besides, the quantitative evolution of damage area during impact is studied, which provides a new perspective for elucidating the damage mechanism. The numerical model is first validated against the available experimental data. The influence of initiation criteria and evolution methods on damage prediction is then performed in two-phase research. The first phase discusses the prediction capabilities of different combinations under single impact. In the second phase, a method for removing residual vibrations under repeated impacts is proposed. The differences caused by the removal and non-removal of residual vibrations are analyzed, and the sensitivity of these differences to various combinations is discussed. Results show that the numerical prediction agrees well with the experiment in dynamic mechanical response curve. Combining Hashin-Strain criterion with linear equivalent strain method and Puck criterion with exponential equivalent displacement method yields optimal results. Moreover, the sensitivity to differences caused by the residual vibrations effects is related to the initiation criterion, and the evolution method.

A critical appraisal of the Hashin failure criterion

The Hashin criterion is one the most popular failure criteria for fibre reinforce composites. It is critically appraised in this paper. The most significant feature of the criterion is failure modes introduced and the assumption that failure is determined by the traction on the failure plane. For this assumption, there has never been any justification provided in the literature, except the available arguments in the Mohr criterion, where the concept of plane failure as opposed to point failure was first introduced based on this assumption. However, the arguments there were applicable only to isotropic materials and, even so, they are not without exceptions. As contradictions to the assumption in the context of composite failure, three relatively simple cases have been considered in this paper, supported by physical evidence. In each case, failure is observed in a plane on which traction vanishes completely, to which the failure cannot be attributed. The assumption is therefore unfounded both theoretically and physically for anisotropic materials, which dismisses the validity of the Hashin criterion in turn.

Predicting the fatigue life of T800 carbon fiber composite structural component based on fatigue experiments of unidirectional laminates

This study is based on the fatigue experiment results of unidirectional laminates and investigates the fatigue performance of T800 carbon fiber/epoxy resin composite structural components through experimental and numerical analysis. Fatigue experiments were performed on [0]16, [90]16, and [±45]8 laminates individually, obtaining the fundamental fatigue parameters necessary for modeling. The fatigue life model for T800 carbon fiber/epoxy resin unidirectional laminates was refined, and fatigue degradation rules were provided for the fatigue progressive damage model. A fatigue progressive damage analysis model for T800 laminates was established based on the 3D Hashin criterion, predicting the fatigue life and fatigue damage failure process of the laminates. A fatigue life prediction model was developed for T800 carbon fiber composite I-beam structural components, which can predict the primary types of fatigue failure, fatigue life and the location of fatigue failure occurrence. The predicted fatigue life of structural components shows good consistency with the experimental results. This method can calculate structural components including ply angles of 0°, 45°, and 90° and obtain the fatigue life contour.

An Insight into the Mechanical Properties of Unidirectional C/C Composites Considering the Effect of Pore Microstructures via Numerical Calculation.

Pores are common defects generated during fabrication, which restrict the application of carbon/carbon (C/C) composites. To quantitatively understand the effects of pores on mechanical strength, this paper proposes a representative volume element model of unidirectional (UD) C/C composites based on the finite element method. The Hashin criterion and exponential degraded rule are used as the failure initiation and evolution of pyrolytic carbon matrices, respectively. Interfacial zones are characterized using the cohesive constitutive. At the same time, periodic boundary conditions are employed to study transverse tensile, compressive, and shear deformations of UD C/C composites. Predicted results are compared with the experimental results, which shows that the proposed model can effectively simulate the transverse mechanical behaviors of UD C/C composites. Based on this model, the effects of microstructural parameters including porosity, pore locations, the distance between two pores, pore clustering, and pore shapes on the mechanical strength are investigated. The results show that porosity markedly reduces the strength as porosity increases. When the porosity increases from 4.59% to 12.5%, the transverse tensile, compressive, and shear strengths decrease by 35.91%, 37.52%, and 30.76%, respectively. Pore locations, the distance between two pores, and pore clustering have little effect on the shear strength of UD C/C composites. For pore shapes, irregular pores more easily lead to stress concentration and matrix failure, which greatly depresses the bearing capacity of UD C/C composites.

Experimental and Simulation Study on Failure of Thermoplastic Carbon Fiber Composite Laminates under Low-Velocity Impact.

Numerous studies have demonstrated that under low-velocity, low-energy impact conditions, although the surface damage to fiber-reinforced composite laminates may be minimal, significant internal damage can occur. Consequently, a progressive damage finite element model was specifically developed for thermoplastic carbon fiber-reinforced composite laminates subjected to low-speed impact loads, with the objective of analyzing the damage behavior of laminates under impacts of varying energy levels. The model utilizes a three-dimensional Hashin criterion for predicting intralayer damage initiation, with cohesive elements based on bilinear traction-separation law for predicting interlaminar delamination initiation, and incorporates a damage constitutive model based on equivalent displacement to characterize fiber damage evolution, along with the B-K criterion for interlaminar damage evolution. The impact response of laminates at energy levels of 5 J, 10 J, 15 J, 20 J, and 25 J was analyzed through numerical simulation, drop-hammer experiments, and XCT non-destructive testing. The results indicated that the simulation outcomes closely correspond with the experimental findings, with both the predicted peak error and absorbed energy error maintained within a 5% margin, and the trends of the mechanical response curves aligning closely with the experimental data. The damage patterns predicted by the numerical simulations were consistent with the results obtained from XCT scans. The study additionally revealed that the impact damage of the laminates primarily stems from interlaminar delamination and intralayer tensile failure. Initial damage typically presents as internal delamination; hence, enhancing interlaminar bonding performance can significantly augment the overall load-bearing capacity of the laminate.

Integrating parametric HFGMC and isogeometric RZT[formula omitted] for multiscale damage modeling of composite structures: A numerical and experimental study

In this research effort, a novel multiscale analysis scheme is proposed for damage modeling of composite laminates, sandwich structures, and stiffened plates relying on capabilities of the parametric HFGMC and isogeometric RZT{3,2} formulations. The Ramberg Osgood (RO) model is incorporated into the micromechanics model to reflect polymer matrix material nonlinearities on the overall homogenized composite behavior. Carbon fibers are assumed to behave in a linear transversely isotropic manner. The higher order RZT{3,2} theory employed at the macro level facilitates efficient applicability of the model to thick composite laminates and soft core sandwiches. On the other hand, it generates all three-dimensional stress components and thus ensures dimensional consistency between micro and macro levels. Numerical discretization and prediction of RZT{3,2} kinematic variables are enabled by performing NURBS based isogeometric analysis (IGA) thereby enhancing modeling efficacy to a significant degree. Soft core plasticity and failure in the composite are evaluated at the macro level through the RO model and Hashin criteria, respectively. Applicability of the method is presented for thin and thick flat composite and sandwich laminates; and further extended to stiffened plates via developing a multipatch formulation. A comprehensive validation of our analysis is conducted by comparing the results with established benchmarks from the literature, experimental data, and three-dimensional finite element method (3D-FEM) simulations. Initially, a moderately thick, simply supported square laminate under transverse loading is examined, a common verification benchmark. Then, results from standard mechanical tests, including tensile, shear, and four-point bending tests on thin laminates, followed by experiments on moderately thick sandwich structures subjected to four-point bending, are presented. Finally, the analysis is extended to a stiffened plate under uniform pressure, demonstrating the method’s accuracy and applicability across diverse structural configurations.

Numerical design of composite material crack arrestors for long-distance gas pipelines

Long-distance gas pipelines are the most common means of transporting natural gas resources. However, the propagation of longitudinal ductile fractures in gas pipelines can result in catastrophic accidents, which must be avoided as much as possible. Crack arrestors can prevent or at least limit the rapid spread of longitudinal cracks by constraining the outwall of pipelines. Carbon fiber-reinforced composite material is one of the best candidates for crack arrestors because of its excellent strength and toughness. However, due to the significant variations in composite material performance, clear design criteria for determining the size of crack arrestors have not yet been developed. This paper presents a comprehensive design procedure for determining the geometrical parameters of composite material crack arrestors based on a finite element model of dynamic pipeline fractures under crack arrestor constraints. Pipeline crack propagation is accomplished using the cohesive zone model, and composite material failure is defined by Hashin criteria. A series of numerical simulations are conducted to assess the ability of crack arrestors to stop a growing crack in a gas pipeline. Ultimately, the minimum wall thickness and axial length of the effective crack arrestor are determined. The proposed design procedure enables the numerical design of composite material crack arrestors and supports safe pipeline operation.

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.

Redefinition of failure envelope of composite materials considering uncertainty of test data

After conducting three World-Wide Failure Exercises (WWFEs), it has become apparent that existing strength theories or criteria have certain deficiencies, and no single theory can accurately match all experimental results. As a result, there is a growing focus on the uncertainties present in the macrocosm test data of composite materials. The paper introduces the concept of uncertainty into the collection of test data for the classical Tsai-Wu failure criterion and Hashin criterion. The method proposed involves fitting the coefficients of the failure criteria by treating experimental data as random variables, a technique that diverges significantly from the conventional method of using composite allowable values to define these coefficients. It also uses the probability of success as a constraint and defines the fitted error as an optimization objective. Monte Carlo sampling is employed to perform a reliability analysis, and six sigma is used for a reliability-based optimization of the failure criteria. The Multi-Island Genetic Algorithm is utilized to search for the optimal value. The approach presented in this study provides the ability to predict future failures in composite materials by considering the uncertainty of the test data. By incorporating uncertainties into the analysis and design process, a more accurate and reliable assessment of the performance of composite materials can be achieved. Moreover, there seems to be a significant difference in the fitting error between the mean data and the normal distribution data. Additionally, when Hashin criterion is modified, the test data matches the failure envelope more closely and the degree of fit between the experimental data and the failure envelope is higher.

Nonlinear analysis model of the progressive damage of aluminum–wood sandwich structures under high-speed impact conditions

The impact responses of various protective structures composed of 2A12 aluminum alloy and wood laminates were studied experimentally. The experiments were conducted using different impact energies. By varying the sandwich material thickness and using two different bullet shapes, the effects of the sandwich material’s damage process and the core layer thickness on the protective performance were studied. The multilayer structure’s core layer failure condition was determined using the improved 3D Hashin criterion and a finite element model was established using Abaqus software. Tensile and three-point bending tests were conducted and the progressive damage model was verified statically. The model was then verified dynamically using the Hopkinson bar test. The mechanical properties of the materials under high dynamic strain rates were obtained through action loading testing of the specimens at different loading rates. The loading waveform was analyzed and a stress-strain relationship diagram was drawn at various strain rates. By verifying the experimental data, a numerical model that could capture the deformation and failure details during crushing was established, and the composite target plate impact failure mode and the trajectory change law were described. This study could lead to use of a new impact damage prediction method for laminates.

Low‐velocity impact response of 3D carbon fiber reinforced polymer auxetic lattice structures

AbstractIn this paper, low‐velocity impact properties and impact damage responses of a novel type of 3D hybrid auxetic structures made from carbon fiber‐reinforced polymer (CFRP) laminates were investigated experimentally and numerically. The structures were first fabricated with three different rib's width ratios t1/t0, and then impacted with three different impact energies of 30, 40, and 50 J using a drop tower impact system equipped with a cylindrical impactor. The finite element (FE) models were built in ABAQUS/Explicit, and the Hashin criteria were applied to predict the failure of the structures. The contact force histories, energy histories, displacements, and failure modes were compared between the experiment and FE simulation at all three impact energy levels. The failure morphologies and mechanisms were obtained and studied. The impact testing results suggest that the 3D auxetic structure with a higher t1/t0 ratio can lead to higher peak contact force and sustain higher impact energy. The failure of the structure starts from the middle area and propagates to the upper and lower areas. This research provides a better understanding of the impact responses and failure modes of the 3D auxetic lattice structure, which can promote the potential applications of the auxetic materials.Highlights Drop weight low‐velocity impact responses of 3D novel hybrid auxetic lattice structures are investigated through both experiment and finite element simulation. The effects of structural parameters on the impact performance of the 3D auxetic structures at different impact energy levels are analyzed. The failure morphologies and mechanisms of the 3D auxetic structures are studied.

Effect of reparation on the mechanical behavior of glass fibers/Elium acrylic laminate composites: Experimental and numerical approaches

AbstractElium® Acrylic/Glass Fiber thermoplastic laminate composites are liable to develop irreversible local defects under quasi‐static loading. To reinforce the damaged material, repair is a cost‐effective mechanical alternative. The present study investigates the tensile behavior of an Elium® glass‐fiber‐based acrylic laminate composite panel, repaired by vacuum bonding with Elium® repair resin and double overlap of external patches (DP). The results obtained for all repaired laminate composites E190/GF_D(10, 20, 30)R with diameters 10, 20, and 30 mm showed an improvement in the mechanical properties of the repaired panels, compared with the drilled and pristine samples. Average load recovery rates were significant for E190/GF_D10R (7.9%, 3.55%, 13%) E190/GF_D20R (23%, 18%, 3.32%), E190/GF_D30R (7.2%, 9.36%, 32.37%) at strain rates of 0.001, 0.01, and 0.05 s−1 respectively. Finite element (FE) models for the virgin, drilled, and repaired composite, performed by coupling the Hashin criteria with the cohesive zone model (CZM), provided a relevant prediction of intra‐ and interlaminar failures of these woven laminated composites.Highlights The effect of vacuum bonding repair with Elium E351 EOT resin was studied. Symmetrical repair of acrylic laminate drilled by fiberglass patches. Tensile strength of the repaired laminates was investigated. Intra‐ and interlaminar damage was predicted by finite elements modeling.

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%.

Widely Employed Constitutive Material Models in Abaqus FEA Software Suite for Simulations of Structures and Their Materials: A Brief Review

The structural response of masonry/concrete structures depends upon the load-carrying mechanism and subsequently deformations produced by loads carried. In masonry/concrete structures, identification of the stress/strain imposing stress conditions and strain hardening/softening makes the structural response more complicated. Elastic damage models or elastic-plastic constitutive laws are inadequate to simulate masonry/concrete response under high strain-rate loadings. Further, irreversible or plastic strain cannot be realized using the elastic damage model. Several constitutive damage models are available in the literature. In this article, a concise explanation of the functioning of different material models in the Abaqus software package has been provided. These models include concrete damage plasticity for concrete and masonry, traction separation constitutive laws for brick-mortar interface, Hashin's criteria for CFRP, Johnson-Cook plasticity for steel, and crushable foam plasticity hardening for metallic foams. Researchers frequently utilize these models for numerical simulations and modeling of infrastructural elements and their respective materials when subjected to various structural loads. Besides, this paper presents a discourse on problem-solving methods and a comparison between explicit and implicit analysis. The research provides valuable input to researchers and practitioners in the field of structural engineering for an in-depth understanding of the functioning of Abaqus' pre-existing material models.

Phenomenological failure criteria analysis of a composite bolted joint under multi-axial loading using the finite element method

Carbon Fiber Reinforced Polymer Composites (CFRP) are commonly used in various sectors due to their excellent properties. However, they present complex failure modes, particularly in bolted joints, which are widely used in the aeronautical industry due to their ease of assembly and disassembly. Phenomenological failure criteria can be used to evaluate failure modes analytically and reduce the number of experimental tests. It is important to determine the criterion that best reflects reality. The Hashin, Puck, and LaRC04 failure criteria were evaluated using a finite element method software - FEMAP 2021.2 educational version - through simulation. Numerical simulations were conducted on a 2D model of a carbon/epoxy composite bolted joint under multiaxial loads, following ASTM D5661 dimensions. The failure criteria were compared to determine the most appropriate one for this type of component. Among the evaluated criteria, the Hashin criterion showed an intermediate level, while the Puck criterion was the most conservative and the LaRC04 criterion was the least conservative. It is recommended to use the Hashin criterion for general analyses. For analyses that require a detailed examination of compression failure modes, it is recommended to use the LaRC04 criterion. The Puck criterion is suggested for more conservative analyses.

ELASTIC AND STRENGTH PARAMETERS DETERMINATION OF POLYMER COMPOSITE MATERIALS AND CYLINDRICAL SHELLS

The article presents a method for layout optimization in polymer composite materials that allows to assess their strength. In order to assess the stress-strain state of each layer, an orthotropic elasticity model is used assuming that the fibers in the material are parallel. The behavior model of polymer composite materials is based on the Hashin criterion, which makes it possible to separate the destruction mechanisms of matrix and fiber. The strength assessment was carried out in accordance with the structural approach involving studying the strength of each layer separately. The parameters of the deformation model and the Hashin strength criterion were determined based on the results of testing. Tests were carried out on unidirectional polymer composite materials samples cut at angles of 0, 90 and 45° to the direction of reinforcement. The verification was based on the results of bending tests of polymer composite materials samples. Verification showed high proximity between the calculation results and the experimental data. A method for selecting the layout angles of each layer of polymer composite materials has been developed making it possible to calculate the greatest strength of the cylindrical shell under various external loads. The method involves determining the stresses in each of the polymer composite materials layers, as well as Hashin indicators corresponding to the destruction of the fiber or matrix under tension or compression. Based on the indicator values, the optimal angle and layout pattern can be selected, providing the greatest margin of safety for the shell. This method allows for a preliminary assessment of the safety factor of cylindrical shells made of polymer composite materials based on the experimentally determined elastic parameters of the material and the parameters of the Hashin strength criterion. The method takes into account the angle and layout of the prepreg under the influence of internal pressure, axial compressive force and torque.

A Method for Predicting the Impact Limit Speed of Composite Laminates Under Different Ambient Temperatures Based on the Three-Dimensional Hashin Criterion

A Method for Predicting the Impact Limit Speed of Composite Laminates Under Different Ambient Temperatures Based on the Three-Dimensional Hashin Criterion

Numerical investigation of the low velocity impact behavior of CFRP laminates

The impact response and failure mechanism of carbon fiber reinforced composite laminates under low velocity impact was investigated using ABAQUS®. A finite element model was developed based on the progressive damage theory to study the impact response of CFRP laminates with hemispherical impactor. The impact tests were conducted on cross-ply (0/90)2s and quasi-isotropic, QI (0/45/-45/90)s laminates with different impact velocities. From the numerical simulation, the damage initiation and propagation in the CFRP laminates were found in terms of damage location, size and shape. The intra-laminar damages such as fiber and matrix damages were predicted using in-built Hashin criterion of ABAQUS®. The traction separation based cohesive surface modelling approach was utilized for capturing the inter-laminar failure initiation and propagation induced by impact loading. The numerical results of different impact energy levels were analysed for different failure modes for varying impact force, displacement and kinetic energy. The total volume of fiber damage and the total area of delamination were calculated for each laminate sequence. From numerical simulations, it was observed that the delamination was less on cohesive surfaces above the mid-thickness plane due to high compression through the thickness. The fiber damage was found at 65 J of impact energy. The first load drop was observed in the cross-ply laminates due to the delamination between lamina 5 and 6. The study revealed that the QI laminates had higher impact resistance and smaller damage zone than the cross-ply laminates.

Study on low-velocity impact response of kevlar/epoxy-polyurethane sandwich panels

This study aims to investigate the maximum energy absorption of sandwich panels featuring composite facesheets and a polyurethane foam core under low-velocity impact. The research explores various impactor head geometries, fiber orientations, and the number of composite layers on the panel facesheets. Three different impactor heads with flat, hemispherical, and conical shapes were used for experimental impacts. Numerical simulations were performed using Abaqus/Explicit finite element software, with damage initiation in the composite layers determined by the three-dimensional Hashin criterion. The results revealed that the conical-head impactor caused the highest energy absorption, accompanied by the greatest displacement and velocity changes. Among specimens with different fiber orientations, the 60° fiber layers exhibited a 9.41% and 8.45% higher maximum force compared to the 30° and 45° fiber layers, respectively. Furthermore, the study investigated the influence of the number of composite layers in the facesheets. It was found that panels with more layers in the bottom facesheet demonstrated a 4.94% increase in energy absorption compared to panels with more layers in the top facesheet. This research provides valuable insights into optimizing sandwich panel designs for enhanced energy absorption during low-velocity impact scenarios.