Hashin Criterion Research Articles

Performance of Carbon Fiber-Reinforced Polymer Plates Against Impact Loading

The carbon-fiber laminated composites are widely used in various industrial sectors due to their magnificent mechanical and engineering properties. While designing the structures of strategic importance, the impact perforation study and prediction of impact performance of such composites are of utmost importance. This work basically concentrates on two major areas of impact perforation study, determining impact perforation characteristics and understanding the perforation process. The objective has been achieved through experimental as well as numerical investigations. Microstructural analysis have also been carried out to understand different energy-absorbing mechanisms. The pneumatic gun setup is utilized to fire the projectile. In addition, square-shaped carbon fiber laminates and projectiles are modeled in ABAQUS/Explicit. The carbon fiber laminates of different thicknesses and layup sequences are impacted with three different types of projectiles. The cross ply, angle ply and quasi-isotropic layup sequences are considered in this study. The conical, blunt and ogive nose with caliber radius head (CRH) 1.5 projectiles are modeled as analytical rigid. Hashin criteria are adopted to replicate the behavior of carbon fiber laminates. The experimental and numerical calculations are compared and are found to be in good agreement. The different perforation features are calculated and the influence of ply orientations, thickness, projectile shape and impact velocities on the performance of targets against impact are discussed. An efficient and better laminate configuration under various ballistic conditions has been sought.

Experiment on the impact response of aluminum alloy wood core sandwich composites

In this work, a protective structure with 2A12T4 aluminum alloy as the panel material and plywood as the core layer was designed. Penetration experiments were performed by firing multiple projectiles from a light gas gun. The impact behavior, damage mode, absorbed energy, and residual strength of the interlayer after impact were studied. The dynamic response and the failure of the interlayer were analyzed. Disbonding, fiber fracture, buckling, shear, and core fracture between the metal layer and the composite layer of the front panel were observed. The impact resistance of the sandwich plate was also studied. Based on the results of the experiments and numerical simulations, failure determination of the plywood core layer was achieved using the Hashin criterion, and a finite element model was established using ABAQUS software. High-speed impact testing was performed with a Hopkinson pressure bar. The stress–strain relationship under a high dynamic strain rate is given here, and the energy absorption efficiency under loading in different directions was analyzed. Finite element analysis of the representative volume elements in the wood microstructure was also carried out. The results reported here can be used to guide optimal design of sandwich structures suitable for use under high-speed impact conditions.

Parametric theoretical prediction of elastic properties and strength of fine weave pierced C/C composites

This paper developed a parametric model of fine weave pierced carbon/carbon (FWPCC) composites based on the structural relationship of actual sample information. The elastic constants and compressive strengths of FWPCC composites with various Z-directional yarn contents were parametrically investigated. The developed theoretical prediction model agreed well with the experimental data. The parametric prediction results found Z-directional modulus of FWPCC composites with 6 K Z-directional yarns increased by 88.21 % compared to FWPCC composites with 1 K Z-directional yarns; X/Y-directional modulus decreased by 17.32 %; Z-directional compressive strength increased by 337.33 %; X/Y-directional compressive strength only decreased by 6.12 %. The accuracy of the two failure criteria (Hoffmann, Hashin failure criterion) used for the model was compared. The accuracy of the model prediction using Hashin failure criterion was better than that of the Hoffmann criterion. The predicted results using Hashin criterion also showed that under Z-directional compressive loading, the composite failure was mainly the compressive failure of the Z-directional yarns; under X/Y-directional compressive loading, the composite failure was mainly the compressive failure of the fibers in the bending section in the X/Y-directional yarns. The developed theoretical model was of great significance for the engineering application of C/C composite.

Buckling and fracture analysis of thick and long composite cylinders with cutouts under axial Compression: An experimental and numerical campaign

This article reports on the manufacturing, experimental testing, and finite element analysis of very thick and long carbon-fiber-reinforced polymers (CFRP) tubes under uniaxial compression (radius-to-thickness ratio ∼ 10 and length-to-radius ratio ∼ 21). Herein, long and hollow axisymmetric composite cylinders were produced through bladder molding. The CFRP tubes have two oppositely located cutouts in the middle of the structures. Three test specimens with different cutout diameters (5, 10, and 15 mm) were experimentally tested until failure. The experimental testing campaign was supported by digital image correlation, acoustic emission, and infrared thermographic measurements to investigate the damage propagation and failure analysis. The CFRP tubes failed at the cutout location due to fiber fracture. Linear static and geometrically non-linear analyses were performed using ABAQUS to analyze the CFPR tubes under axial compression. In general, numerical and experimental results are in good agreement if the maximum stress or Hashin criteria are applied.

An evaluation model of bearing capacity for CFRP connection structure with lightning thermal damage

Connection structure of carbon fiber reinforced plastic (CFRP) is fragile to lightning and its damage form is complex. Its bearing capacity is affected, which should be evaluated to ensure safety after lightning strike. Thus, a model of bearing capacity prediction (BCP) is proposed for CFRP connection structure. Its lightning damage is evaluated from thermal perspective combining joule heat and dynamics failure, which is caused by lightning ablation and the Blow-Off Impulse (BOI) effect, respectively. Electrical thermal coupling and high explosive models are utilized for calculation. Subsequently, lightning thermal damage is inherited by full restart method. The computing efficiency and convergence is improved caused by structural local distortion. Tensile bearing capacity of structure is assessed by employing the strain-based 3D Hashin criterion. A tensile experiment is carried out to verify BCP model. The results show that lightning thermal damage is the worst around current injection region. Tensile-shear and extrusion-shear failures concentrate at CFRP fastener holes under tensile load. Tensile failure load of structure is further reduced by 8.03% due to the BOI effect. The bearing capacity of CFRP connection structure can be accurately predicted by BCP model after lightning strike and deviation is 9.8% from experiment.

Dynamic response and failure of CFRP Kagome lattice core sandwich panels subjected to low-velocity impact

Dynamic response and failure of carbon fiber reinforced plastic (CFRP) Kagome lattice core sandwich panels subjected to low-velocity impact were investigated experimentally and numerically. The geometrical shapes of the impactor noses are flat, hemispherical, and conical. The active failure modes of fiber fracture, matrix crack, delamination of face sheets, rib inclining/fracture of lattice core, and debonding were observed in experiment. The impactor nose shape has significant influence on the failure modes of sandwich panels. The energy absorption of sandwich panel increases with increasing impact velocity. The sandwich panel struck by the flat impactor has the highest energy absorption among three impactor noses. Finite element (FE) simulations implementing a user-defined material subroutine (VUMAT) of Hashin criterion and progressive degradation were performed and agree well with the experimental results. It is shown that both dynamic response and energy absorption of the sandwich panels are sensitive to the impactor size and impact position.

In the ability to extend Hashin criterion for mixed mode I/II fracture assessment of cracked orthotropic materials

In the ability to extend Hashin criterion for mixed mode I/II fracture assessment of cracked orthotropic materials

Experimental and numerical study on the high-velocity hail impact performance of carbon fiber aluminum alloy laminates

The experiment and finite element method (FEM) simulation of high-velocity hail impact on carbon fiber reinforced aluminum alloy laminates (CARALL) were carried out in this paper. CARALL were prepared via an autoclave process after surface anodizing. The properties of the specimens were verified by mechanical properties testing. The light gas gun was employed to conduct the hail impact tests with different impact velocities, impact angles and ply sequences. The surface damage, displacement of the impact center and deformation depth in different test schemes were compared. The FEM model of the high-velocity impact of hail on CARALL was established using ABAQUS/Explicit. The strain-rate dependent model was adopted for hail while the Johnson-Cook damage constitutive model was adopted for the aluminum alloy layer. The 3D Hashin criterion damage model based on fracture energy was applied for the CFRP layer via the VUMAT subroutine. The cohesive element was inserted between the laminates to investigate the interlaminar damage. The accuracy of FEM was verified by comparing with the results obtained by tests. Combined with the energy absorption and internal damage mechanism, the effects of different parameters on the hail impact resistance of CARALL were studied.

Effect of forced assembly on bearing performance of single-lap, countersunk composite bolted joints – Part Ⅱ: Numerical investigation

A progressive damage model with the combination of 3D Hashin criterion and exponential material degradation was developed and validated according to the experimental results of the Part Ⅰ. The effect of forced assembly on stress distribution and bearing damage of single-lap, countersunk composite bolted joints were revealed by utilizing the present model. It is found that the joints with forced assembly show higher contact stress levels. The stress distribution of the countersunk hole tends to be uniform, while that of the non-countersunk hole is more uneven, and the maximum contact stress occurs at the non-countersunk hole. Furthermore, the forced assembly made a bolt sustain additional axial tensile load, introducing high failure risks to the bolts. With forced assembly, the fiber compressive damage and in-plane matrix compressive damage are more serious, and the most serious damage is transferred from the countersunk hole to the non-countersunk hole.

Damage Analysis of CFRP Hybrid Bonded-Bolted Joint during Insertion of Interference-Fit Bolt.

In this study, experiments and finite element analysis (FEA) were used to evaluate the impact of interference-fit sizes on CFRP hybrid bonded-bolted (HBB) joint damage during bolt insertion. The specimens were designed in accordance with the ASTM D5961 standard and bolt insertion tests were performed at selected interference-fit sizes (0.4%, 0.6%, 0.8%, and 1%). Damage to composite laminates was predicted using the Shokrieh-Hashin criterion and Tan's degradation rule via the user subroutine USDFLD, while damage to the adhesive layer was simulated by the Cohesive Zone Model (CZM). The corresponding bolt insertion tests were performed. The variation of insertion force with interference-fit size was discussed. The results showed that matrix compressive failure was the main failure mode. With the growth of the interference-fit size, more failure modes appeared, and the failure region expanded. Regarding the adhesive layer, it did not completely fail at the four interference-fit sizes. This paper will be helpful in designing composite joint structures and especially for understanding CFRP HBB joint damage and failure mechanisms.

Postbuckling behavior and failure prediction of large‐size composite C‐beam under bending‐shear coupling load

AbstractIn this article, a novel experimental device that combines bending and shearing was proposed to investigate the load‐bearing performance of large‐size C‐beam structures against bending‐shear buckling, allowing for the adjustment of bending‐shearing ratio. Three different bending‐shear coupling conditions were performed for test loading, and the strain gauges were carried out to detect the strain distribution for postbuckling performance of the large‐size C‐beam. The finite element models were established by ABAQUS/Explicit to explore the stress distribution and damage evolution during postbuckling failure. Thereafter, the LaRC05 and Hashin criterion was used for failure prediction of the large‐size C‐beam in numerical simulations. The experiment results show that the large‐size C‐beam has excellent postbuckling bearing capacity regardless of bending or shear resistance. Based on the results, the failure numerical model considering the stress distribution in postbuckling and the finite element calculation were in good agreement with experiments. This study can offer a practical reference for the postbuckling performance of large‐size C‐beam structures after bending‐shear coupling.

Study on the O-/ U-type collapse of reinforced thermoplastic pipes (RTPs) subjected to hydrostatic external pressure: Experimental tests and numerical analysis

Due to the anisotropy and progressive failure of composites, the collapse problem of RTPs is more complex compared with that of traditional steel pipes. To address this problem, the collapse behavior of RTPs subjected to external pressure was studied by conducting collapse tests and numerical simulations. Two different collapse modes including the O-type and U-type mode were observed during the collapse tests. It was the first time to observe the U-type collapse mode of RTPs in open literature. For O-type collapse mode, the cross-section turned into an ellipse. And for U-type collapse mode, it turned heart-shaped. Meanwhile, numerical simulations were conducted by combing eigenvalue analysis and arc-length method, in which the progressive failure of composites was considered by employing a fracture energy degradation model based on the Hashin criterion. To simulate the U-type collapse mode, eccentricity was also introduced. Research results indicated that the critical pressure obtained by tests and numerical simulations agreed well for both O-/U-type collapse modes. The collapse process could be described as “contraction-collapse point-large deformation”. It was found that the progressive failure of composites would reduce the pressure-resisting capacity greatly. For the composites, the shear failure, the matrix and fiber compressive failure were dominant failure modes.

Experimental and numerical investigation on the failure behavior of Bouligand laminates under off-axis open-hole tensile loading

The Bouligand structure is a fibrous laminate with uniaxial layers assembled periodically into a helicoidal pattern. Compared to other types of laminates, its resistance to in-plane damage still lacks clarification. The failure behavior of Bouligand laminates under off-axis open-hole tensile (OHT) loading was investigated compared to cross-ply and quasi-isotropic structures using experiment and numerical simulation. After verifying the progressive damage model based on Hashin criteria, the numerical predictions from various off-axis loadings were compared between these three structures. The results show that Bouligand laminates exhibit low but nearly stable OHT strength. In comparison, the cross-ply structure exhibits high OHT strength variation when loaded in different directions. With the change of off-axis angle, the OHT strength of the Bouligand structure changes by 10.1 % from 405.2 MPa to 364.1 MPa, while it changes by 69.1 % from 533.8 MPa to 165.1 MPa for the cross-ply structure. Besides, the Bouligand structure exhibits higher OHT strength when the off-axis angle exceeds 5°. It also exhibits a more stable OHT strength than the quasi-isotropic structure. It is shown that the failure of fiber and matrix is the primary factor affecting the OHT strength of the laminate, while the delamination has little effect on the OHT strength.

Fatigue analysis of wind turbine composite blade using finite element method

In the past 30 years, wind turbine blades (WTB) have undergone significant development, increasing their size and introducing composites into manufacturing processes and using numerical simulation to assess their strength and structural integrity, helped increasing the number of installed wind turbine units as well as reducing the cost of wind generated energy. In this paper a DLoad subroutine was developed to assess monitor and evaluate the structural integrity of a large wind turbine blade under numerous static load scenarios. The fatigue study was carried using the finite element method, and the DLoad subroutine developed was used with ABAQUS finite Element analysis Software, and performed perfectly. The results show that the proposed layup parameters and the chosen composite materials gives to the wind turbine the desired structural strength. Furthermore, the DLoad subroutine for the fatigue study shows that the higher is the applied force the faster the blade fail. While, Hashin Criterion shows that the distribution of damage for the matrix and the fiber is all over the blade, but the failure only occurs after reaching an energy threshold which depends on the composite materials and the layup parameters used. Therefore, the chosen layup model will allow the wind turbine blade to withstand the extreme climatic conditions in the sea.

Repair Parameter Design of Outer Reinforcement Layers of Offshore Wind Turbine Blade Spar Cap Based on Structural and Aerodynamic Analysis

The influence of the outer reinforcement layers on the repair structure and aerodynamic performance was studied. Firstly, a continuous damage mechanics model was established, and the 3D Hashin criterion and cohesive zone material model were used to analyze the damage repair model. The failure load deviation was 5.5%. Secondly, on the basis of the γ−Reθ transition model and SST–ω turbulence model, the aerodynamic analysis model of DU300 airfoil was established. The numerical simulation results showed that the lift coefficient and pressure distribution at the angle of attack of 10° and 15° were deviated from the experimental values by 2%. Furthermore, 27 structural repair models, nine 2D aerodynamic repair models, and a 3D full-scale blade model were designed. It was found that, when the repair length accounted for 60% of the total model length, the failure load increased by 22%, but the aerodynamic power with the repair length of 10 m was decreased by 0.137%. When the repair area was large and the repair height was from 4 mm to 6 mm, the failure load was greatly increased by about 30%, and the aerodynamic pressure distribution and static pressure field fluctuated significantly. The results show that the structural and aerodynamic characteristics were closely related to the repair parameters.

Characterisation of mechanical behaviour of fibre reinforced thermoplastic composites subjected to off-axis compressive loading

This paper presents an experimental and numerical investigation on the mechanisms of damage onset and evolution in unidirectional carbon fibre reinforced thermoplastic (CFRTP) composites subjected to off-axis compressive loadings. A test fixture was designed to prevent buckling, splitting and end collapsing of specimens during test. A series of compression tests were conducted with specimens of various off-axis angles. Different failure mechanisms and nonlinear stress-strain responses were observed and studied. The fracture angles of the tested specimens were evaluated and analysed according to Puck’s theory. The off-axis compression failure envelope based on LaRC05 and Hashin criteria was presented using finite element analysis and compared to experimental results. It is shown that the LaRC05 criterion can provide accurate predictions for matrix cracking failure mode of unidirectional thermoplastic composites controlled by compression-shear combined stresses.

Failure Analysis of T800 Carbon Fiber Composite Joint Structure With Double Bolts

In this paper, the progressive damage model of T800 carbon fiber composite double-bolt joint based on Hashin criterion was established based on the finite element analysis. By changing the bolt diameter, the numerical simulation of the strength change of the joint was carried out. The damage evolution process was studied and the corresponding verification test research was carried out. Finally, the damage and failure process of the T800 carbon fiber composite double-bolt joint is given, and the strength optimization design scheme is proposed.

Dynamic response of composite tube reinforced porous polyurethane structures under underwater blast loading

The hyper-elastic porous structures show excellent acoustic stealth, impact isolation and underwater explosion protection properties when they are subjected to underwater blast loads. But the energy absorption ability of them needs to be improved, which is caused by premature densification. Therefore, the composite reinforced hyper-elastic porous polyurethane structure (CRHPP) filled with carbon fiber composite circular tubes are designed and fabricated in this paper. Based on quasi-static compression test results, it is shown that the CRHPPs has a 407% increase in energy absorption compared to the porous polyurethane structure. The dynamic responses and failure modes of the CRHPPs subjected to underwater blast loads are investigated by tests and simulations. The CEL (Coupled Eulerian-Lagrangian) method combined with the three-dimensional Hashin criterion are used to simulate the response process. In order to further improve the underwater explosion resistance of the CRHPPs, the effects of structural gradient on the responses are simulated and analyzed. The results show that the stiffness and energy absorption capacity of the hyper-elastic porous polyurethane structure can be significantly improved by adding composite tubes. There are no permanent damage and densification in the CRHPPs subjected to far-field underwater blast loads. Whether gradient or uniform in the other layers, these CRHPPs without reinforcement in the front first layer show better underwater explosion resistance and protection effect.

On Quasi-Static and Dynamic Compressive Behaviors of Interlocked Composite Kagome Lattice Structures

Abstract The quasi-static and dynamic compressive behaviors of carbon fiber-reinforced plastic (CFRP) Kagome lattice structures subjected to quasi-static load and low-velocity impact were investigated experimentally and numerically. CFRP Kagome lattice structures were fabricated by using the interlocking method. The quasi-static compression and low-velocity impact experiments were carried out and the failure mechanisms of CFRP Kagome lattice structures were explored. A user-defined material subroutine (VUMAT) involving three-dimensional Hashin criterion and progressive damage evolution was developed and implemented in the refined finite element (FE) model to model the failure of composite lattice structures. Good agreement is achieved between FE simulations and experimental results. It is shown that both in-plane stiffness and the failure mode of CFRP Kagome lattice structure are sensitive to the load directions. CFRP Kagome lattice structures subjected to quasi-static load experience elastic deformation, bending/kinking failure, rib fracture, and structure collapse sequentially. CFRP Kagome lattice structures subjected to low-velocity impact suffer from the multiple fractures at the slots and the maximum peak loads of dynamic response increase with increasing the impact velocity.

Investigation into a comprehensive forming limit curve considering multi-parameters effects for semi-cured FMLs through uniform pressure loading test

Recently, hydroforming has paid dividends in composite forming due to its uniform pressure distribution, which helps in reducing the delamination defects. Considering the need to develop an appropriate criterion for evaluating the formability of FMLs, inspired by sheet metal forming and testing, the uniform pressure loading test was adopted to characterize the formability of semi-cured FMLs by forming limit curve ( FLC). In this paper, both theoretical analysis models considering and ignoring the tangential cohesive effect were established, and the stress expression of the critical zone was given. The results show that the tangential cohesive stress demonstrates a non-negligible influence on the FLC. A new form of comprehensive FLC was given by defining global equivalent strain and global strain ratio and analyzed by the finite element method. In addition, the numerical simulation model and the experimental parameters were verified. A simplified Hashin criterion was proposed and developed into the numerical simulation as a subroutine based on theoretical analysis. Parameters such as blank holder pressure, pressure rate, and temperature were considered both in experiments and simulation. Only fiber stretching damage was distinguished in the cross, single, and arc crack but no wrinkling. As predicted theoretically, a lower forming limit is expected when FMLs are subjected to greater tangential cohesive stress. Finally, with the help of numerical simulation, the influence of different boundary conditions on the comprehensive FLC was studied. Instead of a simple evaluation of FMLs, this comprehensive FLC could be used directly to optimize hydroforming processes in the engineering field.