Value Of Strain Energy Release Rate Research Articles

Investigation of fracture characteristics of titanium/CFRP hybrid composites through experimental and numerical methods

In this study, the delamination resistance of carbon fiber reinforced polymers (CFRP) consolidated with titanium alloy at the interface between the metal and composite was investigated experimentally and numerically. End-notched flexure (ENF) tests were performed to assess the fracture toughness (GIIC) for Mode II crack expansion of Ti6Al4V titanium alloy/CFRP composite parts. The EFN test is applied to Ti6Al4V-carbon fiber/low melt poly (aryl ether ketone) (CF/LM-PAEK) and Ti6Al4V-carbon fiber/poly (ether ketone ketone) (CF/PEKK) composites with the [0°]24 stacking sequence of unidirectional (UD) fibers. Experimental results indicate that the LM-PAEK composites exhibited Mode II strain energy release rate values 27.64 % higher than those of the PEKK composites. The finite element simulation by LS‐DYNA shows good correlations with the experimental results, with an average error of 5.44 % for the PEKK and 10.58 % for the LM-PAEK, respectively.

Mode I fracture behavior of glass fiber composite-steel bonded interface – Experiments and CZM

Debonding is characterized as the governing failure mode in the innovative wrapped composite joints made with glass fiber composite material wrapped around steel hollow sections without welding. The prerequisite for predicting debonding failure of wrapped composite joints is to obtain fracture behavior of the composite-steel bonded interface. The mode I fracture behavior of the bonded interface was experimentally investigated using glass fiber composite-steel double cantilever beam (DCB) specimens. The crack length a and the crack tip opening displacement (CTOD) during the test were accurately measured by analyzing the digital image correlation (DIC) data while the strain energy release rate (SERR) was calculated through the extended global method (EGM). The cohesive zone modeling (CZM) was utilized in the finite element model with the proposal of a four-linear traction-separation law to simulate the mode I fracture process. An approach is introduced to determine the critical stages of the proposed four-linear cohesive law by combining accurate measurements of crack length a and CTOD, along with SERR values. The validity of the four-linear cohesive law and the introduced approach to determine the critical stages were confirmed by good agreement in both global and local behavior between the testing and the FEA results.

Mode I fracture properties of thermally-modified spruce wood (Picea abies) at different moisture contents

ABSTRACT The influence of moisture content and density on fracture properties of unmodified and thermally modified spruce wood (Picea abies) has been investigated. Thermal modification was done at 180 °C, 200 °C, and 230 °C, and samples were conditioned at 20%, 44%, 76%,% and 88% relative humidity. Double cantilever beam specimens with TL and RL orientation were used for testing. The crack length was determined via digital image correlation, and the compliance of the specimen was determined via multiple loading-unloading cycles of the specimen. The strain energy release rate was calculated, which decreased with an increasing degree of modification and increased with increasing wood moisture content. The analysis showed that the strain energy release rate increased more with wood moisture content for unmodified samples, while the dependence of the release rate on moisture was less obvious for modified samples. The strain energy release rate values are higher in the TL orientation than in the RL orientation, while the crack length has no significant influence. The highest strain energy release rate was 0.256 N/mm for the unmodified TL specimens exposed to 88% relative humidity, and the lowest was 0.071 N/mm for the RL orientation of the thermally modified specimens at 230 °C and then exposed to 88% relative humidity. From all measurements, functions were fitted to calculate the strain energy release rate as a function of orientation, degree of modification, moisture content, and density of the spruce wood, which can be used to calculate the strain energy release rate for any combination of the factors studied.

The impact of sterilization, body environment condition and raster orientation on tensile-shear cracking of sub-sized 3D printed specimens

Use of 3D printed parts in biomedical applications has received attention recently. The applied loads, manufacturing pre-processing factors or in vivo conditions may affect the reliability and integrity of such implants. To obtain deeper understand regarding the cracking resistance and microstructure of extrusion-based 3D printed acrylonitrile butadiene styrene (ABS) material a number of sub-sized and short bend beam samples are manufactured. The influence of raster orientation, Gamma radiation sterilization, body environment (saline 0.9% at temperature of 37 °C) and combined Sterilized process & body environment was studied on the mixed-mode I + II fracture toughness and strain energy release rate values. It was observed that exposing the 3D printed ABS material to Gamma-radiation process can increase noticeably the mixed mode fracture resistance compared to the control sample. Printing pattern with raster orientation of ±45° provided a higher mixed-mode fracture envelope compared to pattern of 0/90° for all investigated environments. The microstructure study of SEM pictures obtained from the investigated samples showed dominantly ductile type fracture with some evidences such as formation of dimples and ridge markings. The depth and number of ridge markings and dimples were increased by moving towards mode II (shear mode loading) and for the samples exposed to body environment.

Environment assisted cyclic fatigue crack growth testing of polymer/inorganic laminates under strain energy release rate control

We focus on the development and implementation of an environmental (hot-dry or hot-humid air) testing methodology for adhesively bonded laminates under maximum strain energy release rate (SERR) control. The technique overcomes disadvantages of displacement- and force-controlled fatigue crack growth testing. Fracture mechanics based double cantilever beam (DCB) specimens comprising steel/epoxy- and glass/polyolefin-laminates were investigated using an electrodynamic test system with automated software control. Crack length was evaluated in-situ with a compliance calibration approach. User-defined SERR values were set with a control channel. The SERR was changed every 200,000 cycles or after exceeding crack length milestones. For steel/epoxy-laminates with an adhesive thickness of approximately 5 µm a good agreement of crack growth rates was obtained by displacement and SERR control. Moreover, the negative effect of humidity (50% vs. 10% rh) on the fatigue delamination resistance was confirmed at 60 °C. In contrast, significant deviations of crack growth rates under displacement and SERR control were deduced for glass/polyolefin-laminates with an adhesive thickness of 250 µm under hot-dry (60 °C, 1%rh) conditions. The deviations were attributed to differences in the damage zone size for the soft polymeric adhesive. Under hot-humid (60 °C, 80%rh) conditions a reasonable agreement of displacement and SERR controlled test data was observed and attributed to a less pronounced damage zone and a failure of the glass/polyolefin-laminates in an interfacial manner.

Modelling and finite element analysis of fractured femur bone with locking compression plate under fatigue load condition

Orthopaedic Surgeons are facing difficulties to cure the bone fracture which is developed in the bone of the human due to accidents. Fractured bones are externally joined with the support of screws and locking compression plates. In this present work, the femur bone, locking compression plate and screws were modelled with the help of CREO 2.0 and fatigue analysis was performed for existing joining plate materials using Stainless steel using ANSYS Workbench software. Then crack was generated in the modelled bone and assembled with screws and locking compression plates. Currently used plate materials are replaced with bio compatible materials like Cobalt-chromium (Co-Cr) material, Titanium aluminum Vanadium material (Ti-6Al-4V), 316 Stainless Steel (316 SS) and better and optimum material was identified with improved fatigue life. The finite element analysis was also performed for femur bone with or without Locking compression plates and screws for different implant materials like Cobalt-chromium (Co-Cr) material, Titanium aluminum Vanadium material and 316L stainless steel. Predicted facture toughness and critical strain energy release rate values of femur bone with locking compression plate were 88% and 93% lesser than the predicted facture toughness and critical strain energy release rate values of bone respectively without locking compression plate for 316 SS material. It was observed that the developed crack in the femur bone will not propagate further and it retains the strength of the bone. Predicted fatigue life of the bone for Co-Cr material was higher than 316 SS and Titanium aluminum Vanadium material. Cobalt-chromium alloy implant material was suggested for younger age patients during their bone fracture surgery.

Assessment of the fracture properties of adhesively bonded joints submitted to fatigue loads using the Arcan fixture

AbstractIn the present study, the crack propagation behavior under cyclic loading of an epoxy‐based adhesive was investigated by the means of an Arcan device, in the mixed‐mode plane I+II. The strain energy release rate (SERR) was calculated through an inverse identification method using a Finite Element (FE) modeling. The evolution of the cracked surfaces revealed three main stages during the tests. It was found that under fatigue loading, the crack propagated at a value of SERR per cycle lower than the values of the critical SERR calculated under monotonic loads. The evolutions of the crack propagation rate against the SERR are also provided to highlight the effects of the mixed‐mode ratio on fatigue crack propagation.

Mixed-mode fracture behavior of epoxy-based impact adhesives

The focus of our study was to determine the mixed-mode fracture behavior and the governing fracture (failure) criteria for different impact-resistant/toughened structural adhesives. Four of the five model adhesives used contained organic tougheners in the form of carboxyl terminated butadiene acrylonitrile (CTBN) copolymer, as well as polyurethane adducts. The main crystalline inorganic phases were calcite (CaCO 3 ), wollastonite (CaSiO 3 ) or calcium silicate (CaSiO 3 ), talc (Mg 3 Si 4 O 10 (OH) 2 ), zeolite which is an alumina silicate based mineral and has many different elements in its composition (M 2 /nO.Al 2 O 3 .xSiO 2 .yH 2 O., M can be Mg, Na, Ca, K, Li). The total amount of inorganic fillers was different in each adhesive. Independently Loaded Mixed-Mode Specimen (ILMMS) was used for independent measurement of P I (opening) and P II (in-plane shear) loads which were necessary to determine the strain energy release rate values, G I and G II without using a finite element analysis. Two versions of the ILMMS specimen geometry (a, b) were used: monotonic in opening and static in shear loads, and monotonic in shear and static in opening loads, respectively. Elliptical energy balance failure criterion and parabolic principal stress criterion were used for curve fitting. The experimental data revealed that all but one of the adhesives were more accurately represented by the energy balance criterion except for one that was more accurately represented by the principal stress criterion indicating more brittle behavior. Results obtained from ILLM specimen a showed that ranking varied as related with the G Ic and G IIc values and, also, the applied static load. For example, while Adhesive 2 was in the first rank based on G Ic value, it became third in the ranking based on G II c value. Thus, it can be suggested that ranking as well as the fracture behavior (i.e., cohesive vs. adhesive failure; interfacial separations) change with the extent of the mode mixity present in loading of toughened epoxy adhesives.

Numerical frequency and SERR response of damaged (crack/delamination) multilayered composite under themomechanical loading: An experimental verification

This research predicted the influences of combined damage (delamination and crack) and thermomechanical loading on the modal values and strain energy release rate (SERR) of the curved shell panel. The results are obtained computationally using a computer code (MATLAB platform) with the help of isoparametric finite element (FE) steps and the higher-order deformation polynomial. The Hamilton principle is adopted to obtain the final governing equation for the frequency analysis of the damaged structure. Additionally, the deflection, strain, and stresses are recorded by back substituting the numerical solutions to compute the desired energy values. The obtained solution accuracy and the stabilities are verified by performing the convergence and the comparison (published frequencies and SERR) studies. Moreover, a few lab-scale modal experimentations (cracked laminated composite with and without temperature increments) are carried out to accomplish the proposed model. Lastly, a series of numerical examples related to the SERR and modal responses of the current damaged curved composite structure is solved by considering the geometrical, material, and damage parameters (shape and sizes of delamination and orientation of crack). The SERR values calculated using the virtual crack closure technique. The pointwise comprehensions related to the inputs and the model are envisaged in details.

Numerical prediction of static and vibration responses of damaged (crack and delamination) laminated shell structure: An experimental verification

This research reported the influences of combined damage (delamination and crack) on the layered structure numerically via finite element technique in a higher-order mathematical model framework. In this regard, the modal responses and the strain energy release rate (SERR) are calculated by considering the influences of the delamination and/or crack within the flat/curved laminated structure. Moreover, the virtual crack closure technique (VCCT) has been adopted to compute the structural responses of the layer cracked composite structure, i.e., the SERR values. Further, the exactness of the present model is proven by comparing the frequency and SERR values with the previously published data from the open domain. Additionally, the model validity is certified through the different comparisons with in-house recorded experimental eigenvalues. The composite shell structures are examined for eigenvalue and SERR to assess the effects of delamination and/or crack by altering the input variables to show the applicability of the present model.

Steel plate cold commercial - carbon fiber reinforced plastics hybrid laminates for automotive applications: curing perspective with thermal residual effect

The curing effect on hybrid materials consisting of steel plate cold commercial - carbon fiber reinforced plastics (SPCC-CFRP) hybrid laminates that have potential applications in automobile structures were evaluated in the present study. Specimens with stacking sequences consists of one SPCC plate and six layers of CFRP ([SPCC/[0] 6 ]) under a double cantilever beam (DCB) test were investigated experimentally and analytically. The characterization was performed using a differential scanning calorimetry (DSC) and fourier transform infrared (FTIR) analysis. The specimens were exposed to two different curing times to observe the different strain energy release rates. The results show specimens with a curing time of three hours have stability in strain energy release rate value compared to one-hour curing time. However, in the early stage of fracture, the fracture toughness of 1-hour has a higher value than 3-hour. The critical crack length in this study occurred between 40 and 70 mm. Furthermore, the average strain energy release rate value of G I in 1-hour and 3-hour curing time from the crack length between 98 and 104 mm was 116.6687 J/m 2 based on compliance calibration (CC) method, 113.3966 J/m 2 based on correction factor, and 116.3831 J/m 2 from considering temperature effect theory compared to 1-hour curing time with 81.3232; 79.1026; and 81.0376 J/m 2 , respectively. Based on this study, the fracture toughness and energy release rate of hybrid laminate significantly affected by the curing conditions during the manufacturing process.

Effect of pre-embedded adhesion failures and surface ply delaminations on the structural integrity of adhesively bonded single lap joints made with curved laminated FRP composite panels

This paper investigates fracture mechanics based design of the adhesively bonded Single Lap Joint (SLJ) made with curved Fibre Reinforced Plastic (FRP) composite adherends having pre-embedded adhesion failures and surface ply delaminations at either end of the lap portion. The propagation of pre-embedded through-the-width delaminations and adhesion failures in the SLJ under uniaxial tensile load has been characterized by computing the Strain Energy Release Rates (SERR) near the adhesion failure/delamination fronts. The Virtual Crack Closure Technique (VCCT) has been used for the computation of SERR. Three Dimensional (3-D) non-linear Finite Element (FE) analyses of the SLJ have been carried out for these defects existing either individually or simultaneously at different locations. The predominant modes of failure, the radial location from where these defects may start to grow have been identified. The propagations of adhesion failures have been studied at the interfaces of the adhesive and the adherends by pre-embedding them in the region of high-stress concentrations. Similarly, the propagations of the delaminations are investigated by pre-embedding them beneath the surface ply of both the adherends at the vicinities of the overlap ends. The vulnerabilities of these damage fronts are compared at different locations in the joint for the overall assessment of the structural integrity of the SLJ. The longitudinal shearing mode of adhesion failure is the dominant mode irrespective of their position. The adhesion failure in the lap adherend is more detrimental than the adhesion failure pre-embedded in a similar location at the interface of the strap adherend with the adhesive. The influence of the locations of delaminations when they grow in size on the structural integrity of the joint has also been analysed. The maximum values of SERRs and their radial locations in all the delamination fronts at several locations have been pointed out for structural design purposes. The dominating mode of failure in delamination fronts is highly sensitive to their locations. The growth rates are found to be significantly different in the lap and the strap adherends even for similar locations. It has been observed that the initially straight damage front will gradually tend to be curved in shape.

Effect of edge and internal cracks in 8YSZ thermal barrier coatings subjected to mechanical loading: An numerical approach

Abstract The paper presents fracture parameters for edge and internal cracks subjected to mechanical load by the finite element method. The influence of crack length and crack position on edge and internal crack in TBCs on the strain energy release rate (SERR) and stress intensity factor (SIF) are discussed in detail. The numerical results show that the edge crack near the top surface results in high SERR and SIF mode I. In edge crack, the decreasing trend in the SERR was observed with a decrease in crack length and crack position change towards the TC/BC interface. About 60.06% reduction in the SERR was observed for 100 µm edge crack positioned near the top surface when shifted towards TC/BC interface. Similarly, 60 µm and 80 µm edge crack show a 30% and 56% reduction in SERR. Whereas, 20 µm and 40 µm edge crack shows 1.76 and 1.48 times more value of SERR. The internal crack shows a small value of SERR and SIF mode I irrespective of crack length and position compared to edge crack. For internal crack, as the crack length was increased from 20 µm to 100 µm, the reduction in SERR value increases from 59.23% to 90.23%. Similarly, the edge crack shows high SIF mode I compared to internal cracks irrespective of crack length and position. The edge crack appears to be more unstable than the internal crack and propagates early to cause the failure. The crack length and position strongly influence the crack initiation and propagation, resulting in the failure mechanism.

Comparison of fracture behaviour of a composite laminate with Cross-ply & Angle ply lay-up subjected to Thermal rise loading

Abstract There is an increased usage of advanced composite structures due to several inherent benefits that they offer in comparison with the monolithic materials. But the application of these materials is being limited by the fact that the knowledge about the crack propagation and strength behaviour under application of loads and environmental conditions is not extensive. So, undertaking research in this direction is still very much important. In this paper, a circular crack which is present in the middle of a composite laminate made up with a cross-ply (0/90) and Angle-ply (-45/+45) was modelled and then subjected to thermal loading conditions where the temperature was considered to be rising to study the fracture behaviour. The fracture behaviour of the composite laminate was studied using the strain energy release rate (SERR) value calculated using Virtual crack closure technique (VCCT). Comparison of fracture behaviour between the cross-ply and angle-ply layups the thermal loading conditions on the SERR value in the 3 different modes of fracture with a circular crack located in the middle of the composite laminate was studied and the influence of these parameter was discussed in this paper

Study of fracture behaviour of a composite laminate with central circular hole subjected to thermo-mechanical loading with Temperature fall

Abstract There is an increased usage of advanced composite structures due to several inherent benefits that they offer in comparison with the monolithic materials. But the application of these materials is being limited by the fact that the knowledge about the crack propagation and strength behaviour under application of loads and environmental conditions is not extensive. So, undertaking research in this direction is still very much important. In this paper, a circular crack which is present in the middle of a composite laminate was modelled and then subjected to combined (temperature + pressure) loading conditions where the temperature was considered to be falling and pressure remaining constant to study the fracture behaviour. The fracture behaviour of the composite laminate was studied using the strain energy release rate (SERR) value calculated using Virtual crack closure technique (VCCT). The effect of temperature fall, fiber angle and the combined thermo-mechanical loading conditions on the SERR value in the 3 different modes of fracture with a circular crack located in the middle of the composite laminate was studied and the influence of these parameter was discussed in this paper

Numerical modeling and prediction of adhesion failure of adhesively bonded composite T-Joint structure

This study is reported the adhesion failure in adhesive bonded composite and specifically for the T-joint structure. Three-dimensional finite element analysis has been performed using a commercial tool and the necessary outcomes are obtained via an eight noded solid element (Solid 185-element) from the library of ANSYS. The structural analysis input has been incurred through ANSYS parametric design language (APDL) code. The normal and shear stress distributions along different layers of the joint structure have been evaluated as the final outcomes. Based on the stress distributions, failure location in the composite joint structure has been identified by using the Tsai-Wu stress failure criterion. It has been found that the failure index is maximum at the interface between flange and web part of the joint (top layer) which indicates the probable location of failure initiation. This kind of failures are considered as adhesion failure and the failure propagation is governed by strain energy release rate (SERR) of fracture mechanics. The different adhesion failure lengths are also considered at the failure location to calculate the SERR values i.e. mode I fracture (opening), mode II fracture (sliding) and mode III fracture (tearing) along the failure front. Also, virtual crack closure technique (VCCT) principle of fracture mechanics steps is used to calculate the above said SERRs. It is found that the mode I SERR is more dominating compared to other two modes of failure for the joint considered. Finally, the influences of various parametric (geometrical and material) effect on SERR of the joint structure are evaluated and discussed in details.

Influence of curved delamination front on R-curve of DCB specimen

This work investigated the evolution of the non-uniform distribution of Mode-I strain energy release rate (SERR) along a straight pre-crack front of double cantilever beams (DCB), caused by the anticlastic deformation and the longitudinal free-edge effects. A modified DCB specimen with a curved pre-crack front was introduced in order to alleviate this problem and produce an uniform SERR distribution at the initiation and propagation stages. The first order optimization method was used to determine the appropriate shape of the curved pre-crack front in order to guarantee an uniform SERR during the fracture process. The introduced DCB specimen configuration with the curved pre-crack front was shown to be more convenient for the estimation of a consistent SERR value throughout the fracture procedure without been affected by the visual deviation of the crack length and the non-uniformity ratio of Mode-I SEE distribution along the crack front.

Three-dimensional adhesion failure analysis of the single lap joint having pre-embedded circular defects

The present research aims to study the growth of the circular adhesion failure pre-existing at the interfaces of the strap adherend and the adhesive in a single lap joint. Three-dimensional nonlinear finite element analysis of adhesively bonded single lap joints made with high strength steel adherends under uniformly applied extension have been carried out. The interfacial stresses and strain energy release rate values, being indicative parameters, in the growth of the adhesion failures are computed in the vicinity of the pre-existing circular adhesion failure fronts when the load on single lap joint increases till failure. The magnitudes of the strain energy release rate are computed using the virtual crack closure technique. The results show that the sizes of the adhesion failure significantly influence the magnitudes of the interfacial stresses, the three modes of strain energy release rates and the load-bearing capacity of the single lap joint. The finite element analysis predicts that pre-embedded circular adhesion failures will not have grown from the pre-embedded circular adhesion failure front, instead the failure will be initiated from the overlap ends upon loading for the adhesive bonded single lap joint made with strong adherends and AV119 adhesive. The finite element analysis also proposes a method to calculate the strength of this type of joint configurations using the global shear strength of the adhesive and the intact bonded area. The finite element analysis predicted failure strength of the single lap joint is in good agreement with the experimentally obtained strength for the single lap joint containing pre-existing circular adhesion failure.

Strain energy release rate of sandwich composite beams for different densities and geometry parameters

In this paper, fracture behaviour of marine sandwich structured composite beams manufactured by vacuum-assisted resin infusion process with a PVC foam core, and different thicknesses of upper and lower glass fibre-reinforced polymer face sheets have been investigated. Fracture toughness in terms of strain energy release rate of sandwich composite beam is obtained using three end notched flexure test (3 ENF) by analytical method, finite element simulation using J integral and virtual crack closure technique (VCCT). Experimental testing has been applied with more accurate loading values for finite element modelling (FEM) simulations. The good agreement between experimental and numerical results shows that the finite element model is acceptable. A parametric study is carried out to observe the effects of core thickness, density of core, length of specimens, loading directions of the specimens on strain energy release rate (SERR) of sandwich composite beams under mode II loading. It is developed for the different core thicknesses with varying density combinations. The variations of maximum SERR value are presented graphically using numerical method and compared with analytical solution.

Critical strain energy release rate for rubbers: single edge notch tension versus pure shear tests

In order to estimate mode I fracture strain energy release rate of a rubber upon monotonic loadings, the material is submitted to pure shear and single edge notch tension tests. Catastrophic failure happens suddenly for both tests, revealing mirror-like crack surfaces, assessing the fragile fracture. Nonetheless, Griffith failure analysis could be carried out on pure shear tests only. This analysis leads to an energy release rate value that allows challenging approximate expressions existing in the literature for pure shear and single edge notch tension tests. The pure shear approximate expression provides quantities that match the Griffith analysis. Meanwhile, the strain energy release rate values calculated directly from the single edge notch tension tests differ significantly from the values obtained in pure shear. This discrepancy is explored and possible explanations are discussed showing that pure shear tests should be favored.