Critical Strain Energy Release Rate Research Articles

Experimental research on the fracture of Laminated bamboo lumber using compact tension specimens based on the net section method and digital image correlation technique

This investigation evaluates the significance of thickness (B) and initial crack length-to-width ratio (α) on the fracture toughness of Laminated bamboo lumber (LBL) compact tension (CT) specimens under mode Ⅰ fracture conditions. The digital image correlation (DIC) technique is employed to analyse the result, while the net section method is utilised to determine the critical strain energy release rate (GIc). The fracture mode observed in LBL is characterised as brittle fracture, and the critical stress intensity factor (KIc) of CT specimens achieved a maximum value of 25.58 MPa·mm1/2. The fracture energy, calculated by the net section method, was determined by analysing the crack extension length (ae) of the CT specimen obtained by the DIC technique. This study aims to establish the mathematical connection between GIc, ae, and critical load (PQ) in terms of the strain energy release rate context, which offers an innovative approach to analysing GIc data of CT specimens subjected to mode I fracture. The calculated value for GIc was determined to be 12.18 J/mm2.

Field performance validation of the Louisiana balanced asphalt mix design framework

The balanced mix design (BMD) approach was implemented by agencies to complement the volumetric mix design method. The BMD approach addresses typical pavement distresses using mechanical tests. This study aimed to validate the Hamburg Wheel Track (HWT) rut depth and Semi Circular Bend (SCB) critical strain-energy release rate (Jc) thresholds specified in the Louisiana BMD framework. Seven field projects, including 13 pavement sections with 8–18 service years, were evaluated. Field distress data showed that the maximum HWT rut depth and minimum SCB Jc thresholds are effective parameters for assessing rutting and cracking performance, respectively.

The effect of loading rate on mixed mode I/II fracture behavior of adhesively bonded joints: Experimental and numerical approach

In this study, the use of a modified Arcan fixture to investigate the fracture behavior of adhesively bonded Al/Al joints has been discussed under rate-dependent loading in various loading conditions (mode I, mode II, and mixed mode (I/II)). It was observed that the testing speed has a significant effect on the fracture properties of the joints, especially in pure mode, II. The results indicated that failure load was increased for all three loading modes and an increase was also observed for strain energy release rate at all loading conditions. The critical fracture loads obtained from the experimental tests were used to calculate the values of the critical stress intensity factors and strain energy release rates for loading modes I, II, and mixed mode I/II at different loading rates by using the finite element method. It was shown that the values of strain energy release rate for loading mode II were higher than mode I and mixed mode at all loading speeds. Finally, scanning electron microscope analyses (SEM) were used to investigate the effects of loading speed on the failure surfaces of the adhesive in microstructural scales and it was shown that at low loading rates, the number of crazes that cause failure in the adhesive layer increases.

Investigating the ductile to brittle transition phenomenon in binary Fe-Ni systems using molecular dynamics simulation

Ductile to brittle transition (DBT) phenomenon is commonly observed in BCC Fe-based systems, which significantly deteriorates their low temperature fracture toughness. Ni is known to be an effective alloying element to improve the low temperature toughness by reducing the ductile to brittle transition temperature (DBTT). The present article investigates the role of Ni in tailoring the DBT curve of BCC Fe by employing molecular dynamics (MD) simulation. Here, we performed mode-I loading of different pre-cracked systems (pure Fe, Fe-2 wt% Ni and Fe-4 wt% Ni alloys) over a temperature range of 1–800 K to construct their DBT curves. The DBT curves are subsequently correlated with the temperature sensitivity of fracture stress, which is estimated using the concept of critical strain energy release rate (GIC). The role of Ni in reducing the fracture stress sensitivity is responsible for decreasing the DBTT as well as the slope of the DBT region. The underlying mechanism is discussed in terms of the crack blunting effect of Ni which effectively increases the GIC and hence the fracture stress, particularly at the low temperature regimes. Besides, the significantly large strain rate imposed in MD simulation is mainly responsible for the higher DBTT values when compared with the experimental results. The present paper tackles this strain rate issue by using an appropriate strain rate sensitivity factor to rescale the simulated DBTT values down to the experimental ones, resulting in a good match between the simulated and experimental DBTT.

A phase field and machining-learning approach for rapid and accurate prediction of composites failure

A new approach is proposed for rapid and accurate prediction for composite failure in combination of the phase field and machine-learning methods. First, using experimentally-fitted tangent modulus instead of elastic modulus as constitutive relationship, a modified phase field method (MPFM) is established for the crack propagation and mechanical response, which can be effectively applied for composites with a nonlinear constitutive relationship. Interestingly, both the crack propagation path and mechanical responses of two typical examples of composites using MPFM are well consistent with previously available experimental and calculated ones. Furthermore, the data-driven back propagation neural network (BPNN) is constructed to greatly accelerate the prediction on a database generated by MPFM, emphasizing several critical parameters, for example, fiber orientations, external load, maximum failure strain, and critical strain energy release rate. Of much importance, the well-trained BPNN builds a bridge between the traditional computational fracture mechanics and machine learning algorithms, enabling non-specialists to accurately calculate the mechanical response of composites, moreover, saving over 99% of computing time in comparison with MPFM.

Effects of Thermal-Moisture Coupled Field on Delamination Behavior of Electronic Packaging

Abstract Delamination failure is one of the most prevalent and serious reliability issues in micro-electronic packaging. To understand this phenomenon further, this study constructs an experimental test system consisting of a double cantilever beam (DCB) fixture, an MTS-Acumen microforce tester, and a temperature and humidity controller. The system is employed to investigate the effects of coupled moisture-thermal loading on the critical strain energy release rate (SERR) at the epoxy molding compound (EMC)/Cu leadframe (LF) interface of a very thin quad flat no-lead package (WQFN) assembly. A three-dimensional computational model with hygro-thermal loading conditions is developed to evaluate the moisture diffusion, thermal stress, and integrated stress of a multichip WQFN package under typical processing conditions and precondition tests. The validated simulation model is then applied with the virtual crack closure technique (VCCT) to investigate the fracture behavior at the EMC/Cu LF interface in the WQFN package. The effects of three design parameters on the SERR performance of the package are identified through a parametric analysis. Finally, a Genetic Algorithm (GA) optimization method is employed to examine the effects of the main structural design parameters of the WQFN package on its delamination reliability. The results are used to determine the optimal packaging design that minimizes the SERR and hence enhances the package reliability.

Fracture parameters of woven jute fibre reinforced axial flow fan blade material: an experimental investigation and FEA analysis

Airflow required for the heat and mass transfer in industrial applications is often provided by axial flow fans. Glass fibre reinforced polymers (GFRP) are most often used to make these fan blades. The usage of glass fibres in composite materials is growing. By 2025, the global market for glass fibres will be worth 16.5 billion pounds. However, non-biodegradable composite reinforcement has major ecological and human health concerns, especially when reaching the end of its operational lifespan. Until now, industries have shown a strong inclination to use GFRP without adequately contemplating the potential consequences associated with their disposal. The economic viability of glass fibre recycling is questionable. However, natural fibres like jute and fibres extracted from vegetable plants are of much popular among academics and researchers due to their sustainability and ease of use. So, they’re suitable for making polymer composites. The amount of natural fibres that may be added to GFRP composites without materially altering their mechanical characteristics is a crucial factor in improving their decreased embodied emissions and biodegradability after service life. In this work the material represents an 18-ft axial flow fan blade material made of GFRP. This study used the term denotes the specific material utilised in the fabrication of 18-feet axial flow fan blades for industrial purposes. By substituting one layer of with woven jute and changing its position in it, the materials through are produced. All the materials are tested for fracture parameters like plane strain fracture toughness and Critical strain energy release rate as per ASTM D-5045. The results were validated by using finite element models implemented in a commercially available software ANSYS R19.2. The optimal layup sequence for fan blade material with single-layer woven jute reinforcement was found, which preserves fracture properties, also improves biodegradability after service life.

In-situ fracture toughness measurement of multilayer graphene

Understanding the fracture and failure properties of graphene is a critical step towards integrating graphene into electromechanical devices and flexible electronics. However, the exact fracture properties of graphene are hard to measure due to the atomic level thickness of graphene and its brittle nature which tends to cause it to break before accurate measurements of its properties can be made. In this paper, a method is presented for measuring the fracture properties of graphene with varying number of layers. This method utilizes a custom designed MEMS tensile tester and an effective and repeatable graphene transfer process that enables the transfer of patterned graphene structures onto MEMS devices. The fracture properties of graphene samples with different numbers of graphene layers were tested and the critical strain energy release rate of fracture was measured to be 22 J/m2, 71.3 J/m2, and 145 J/m2 for ∼ 7 layer, ∼12 layer, and ∼ 15 layer graphene, respectively. These results show that the fracture toughness of the graphene increases as the number of layers increases. This is likely due to the need for brittle cracks to propagate through multiple, weakly connected layers of the graphene for ultimate failure to occur in the graphene.

Experimental study of delamination process in elastically coupled laminates with the acoustic emission technique

This paper aims at experimental study of delamination process in multidirectional composite laminate exhibiting elastic couplings by using the acoustic emission (AE) technique. The mode I double cantilever beam (DCB) test was conducted on carbon/epoxy laminate with the bending-twisting elastic couplings according to the ASTM D5528 Standard. Experimental research was supported with visual high resolution registration of propagated crack tip, as well as with measurements of elastic waves generated by developing internal damages by using the acoustic emission set Vallen AMSY-5 equipped with two piezoelectric sensors. Prior to test, values of fundamental Lamb wave modes velocities were estimated and the dispersion curves were calculated. Delamination initiation point was determined by using two different AE criteria. The mode I critical strain energy release rates were calculated by using three different data reduction schemes. Different damage mechanisms during crack propagation process were quantitatively evaluated by fundamental waveform features divided into three characteristic frequency bands groups. In addition, signal energy concentration regions were assessed by using the wavelet transforms. The outcomes revealed various damage mechanisms related with delamination process, even though the matrix cracking found to be the dominating mode of failure.

A Comparison Study on Toughening Vinyl Ester Resins Using Different Nanocarbon Materials.

This study aims to comprehensively compare and evaluate the toughening effects of different nanocarbon materials on vinyl ester resins. Four typical nanocarbon materials, including graphene, graphene oxide (GO), single-walled carbon nanotubes (SWCNTs), and multi-walled carbon nanotubes (MWCNTs), were used as reinforcing fillers for vinyl ester resins. These four nanocarbon materials were dispersed in the vinyl ester resin matrix by the combination of high-speed stirring and probe sonication, and their dispersion states were observed with optical microscopy. The effects of incorporating different nanocarbon materials on the viscosities, thermal properties, tensile properties, and fracture toughness of the resulting modified vinyl ester resins were systematically investigated. The results indicate that the four nanocarbon materials show enhanced toughening effects on the vinyl ester resin in the sequence of SWCNTs, GO, MWCNTs, and graphene. Compared with the control resin, the modified vinyl ester resin containing 0.2 wt% graphene shows 45% and 54% enhancements in the critical stress intensity factor (KIC) and critical strain energy release rate (GIC), respectively. The incorporation of the four nanocarbon materials has almost no effect on the glass transition temperatures of the resulting modified vinyl ester resins. This study provides valuable insights into the selection of nanocarbon additives for enhancing the toughness of vinyl ester resins.

Fracture prediction of solder joints using two-parameter fracture mechanics

Two-parameter fracture mechanics theory is a novel approach to investigate the fracture behavior of solder joints. The present study showed that the single-parameter fracture mechanics was not valid for evaluating the fracture behavior of these joints. Therefore, the ability of the two-parameter (J-Q) fracture mechanics method was assessed. J (critical strain energy release rate) and Q (The constraint parameter) parameters were calculated for the double cantilever beam (DCB) specimens. The two-parameter fracture mechanics theory was observed to be valid for the DCB specimens examined in this research. The J-Q loci extracted from two distinct experimental data sets (adherend thickness and loading arm variation) were coincident. The overlap of two J-Q locus curves indicates the uniqueness of the J-Q locus and capability to predict fracture load.

Fracture toughness evaluation of a nuclear graphite with non-linear elastic properties by 3D imaging and inverse finite element analysis

Effective small specimen tests are needed to obtain fracture toughness and elastic properties as the limited availability of irradiated graphite restricts the quantity and dimensions of test specimens. Both properties have evaluated simultaneously in a crack propagation test with the double cleavage drilled compression (DCDC) specimen geometry of a fine-grained graphite (SNG742) that has non-linear elastic properties in the unirradiated condition. Three-dimensional displacement fields were obtained by digital volume correlation of in situ laboratory X-ray computed tomographs, and the 3D crack geometry (crack tip position, crack opening displacements and angle) was determined objectively by a wavelet variance method. The tensile softening of the Young modulus was determined by inverse analysis of the strain field using the finite element model updating (FEMU) method. The strain energy release rate of the quasi-static propagating crack was calculated using the contour integral method in a finite element model with the derived non-linear elastic properties and the measured displacements as boundary conditions. The critical strain energy release rate was constant with crack length (118 ± 14 J m−2) and equivalent to a fracture toughness of 1.13 ± 0.07 MPa m1/2.

A phase‐field formulation based on an extended F‐criterion for rock fracture

AbstractIn this paper a phase‐field formulation based on an extended F‐criterion (the normalized strain energy release rate criterion) is proposed to simulate tensile‐compressive‐shear rock fractures. By applying the F‐criterion, the phase‐field crack‐driving energy decomposition is determined by a direction search which maximizes the local fracture dissipation. In compressive‐shear states, the computation is supplemented by an explicitly expressed confinement‐dependent mode‐II fracture energy release rate, and the cracking angle is determined by both the fracture energy and strain states. The hybrid formulation and alternate minimization algorithm are adopted for the numerical examples in this paper. Fractures for rock and rock‐like specimens subjected to compression demonstrate the ability of the present model in capturing tensile‐compressive‐shear rock fracture behaviors.

In situ X-ray computed micro-tomography imaging of failure processes in Cr-coated Zircaloy nuclear fuel cladding materials

Chromium (Cr)-coated Zircaloy fuel cladding has been considered a promising candidate materials system for accident tolerant fuels. In this work, two types of Cr coatings produced by cold sprayed (CS) and physical vapour deposited (PVD) methods were studied. In particular, a novel combination of C-ring compression tests at room temperature (RT) and 345 °C in an inert gas environment and real-time X-ray micro-computed tomography (XCT) imaging was adopted to investigate the failure processes. Before testing, the crystal structure and local properties were fully characterized; post testing, ex situ scanning electron microscope (SEM) imaging were conducted to complement the XCT measurements in crack density. It was found that the failure processes in both coatings vary with temperature, as discussed in detail. The hoop strength of first coating cracks’ formation of CS materials were higher than the PVD materials due to their higher interfacial roughness and distribution of splatted grains in CS coating. Based on a calculation of the first Dundurs’ parameter from the measured local properties and observed crack arrest/deflection at coating/substrate interface, it was found that the cold sprayed coating-cladding material system has a higher interfacial toughness in terms of critical strain energy release rate due to its interlocking interfacial structure.

Parametric investigation of bonded composite joints under Mode II using a new methodology based on design of experiments

ABSTRACT In the pursuit of a sustainable future with limited resources and growing environmental concerns, adhesive joining stands out as a pivotal technology for the advancement of lightweight structures. This study aims to investigate the influence of various variables on the critical strain energy release rate in mode II (GIIc) for End-Notched Flexure (ENF) bonded composite joints, employing a new methodology based on Design of Experiments (DoE) approach. Two-dimensional finite element models of the ENF bonded composite joints are developed using commercial software, with all numerical models generated via Python™ scripts linked with AbaqusⓇ. Eleven design parameters related to the specimen geometry and material properties are systematically evaluated to determine the influence of each variable on GIIc. Numerical force–displacement curves are obtained, followed by the application of the Compliance-Based Beam Method (CBBM) to estimate the critical fracture energy in mode II, represented by a numerical envelope. The influence of each parameter is assessed using the main effect (ME) metric. The top five most influential variables affecting GIIc and CBBM are identified as the adhesive’s critical strain energy release rate in mode II (GIIc), effective laminate longitudinal elastic modulus (), adhesive thickness (tA), adherent thickness (h), and pre-crack length (). Furthermore, the study highlights the epistemic uncertainty associated with the geometric variables. Despite the limitations inherent in the computational model, the Plackett-Burman method consistently proves effective in conducting sensitivity analysis of the variables in the ENF test. These findings demonstrate promising prospects for the application of this procedure in the design of composite joint structures.

Experimental characterization of tensile and compressive translaminar fracture toughness coupling multi-physics measurements

The study of the failure modes of carbon fiber reinforced polymers is essential due to their extensive use in industry. Translaminar failure (at the scale of the laminate) has been studied extensively the main goal being to compute the critical strain energy release rate in mode I of the ply GIC_ply but large variations can be observed between papers. This study investigates this failure mode of a carbon/epoxy laminate, using Compact Tension (CT) and Compact Compression (CC) specimens. The stacking sequence used is [45/-45/(0/90)4]s where 45° plies on the outside efficiently prevented the buckling of the specimen to be observed, as well as plasticity of the matrix. Moreover, this layup is rather similar to real-life industrial stacking sequences. Strains fields and axes displacement were obtained using digital image correlation. Infrared images were used to follow the crack propagation during the loading of the specimen and compared to DIC and X-ray tomography crack length measurements. IR measurements studied from a qualitative point of view were thus shown to be an efficient and reliable method. GIC of the laminate GIC_lam was computed with both the ASTM-E399 and compliance methods, and finally GIC_ply was computed using a rule of mixtures. Secondary damage was detected and its effects on the energy dissipated were quantified using strain fields, X-ray and infrared images. This enabled a more accurate rule of mixtures to be redefined. The failure scenarios of all specimens were eventually exhibited. GIC_ply values in tension were found to be higher than in the literature whereas in compression it was found to be lower than in the literature, due to crack propagation being detected earlier by means of IR measurements.

Simulation of fluid driven crack propagation along metal/elastomer interface - Application to the numerical analysis of the rubber cord adhesion inflation test

The Rubber Cord Adhesion Inflation Test (RCAIT) has been proposed as an alternative technique to more standard pull out protocols such as H, T or pull out tests for characterizing the adhesion between cord/cable reinforcement and rubber. During this test, a fluid is injected in between a wire and a rubber cylindrical envelope to provoke the interface separation once a critical pressure is reached. A simple energy balance analysis is used to evaluate the critical strain energy release rate, GC, which drives the crack propagation from measurable quantities. However, some assumptions should be assessed to ensure reliable GC evaluation. Then, a predictive finite elements simulation of the RCAIT is proposed to simulate the fluid driven crack nucleation and propagation process along the rubber cord interface. These results are compared with the ones obtained from the RCAIT simplified analysis.

Enhanced interlaminar mechanical behavior of advanced fiber metal laminates via nano Al2O3‐IPN formation and surface pre‐treatments

AbstractThe inferior delamination resistance and out‐of‐plane performance of fiber metal laminates (FMLs) are of serious concerns. This work employs two modification methods, namely metal surface's chemical pre‐treatment and nano Al2O3 embedded interpenetrating polymer network (IPN) formation for improving the delamination resistance of aluminum and glass fiber‐reinforced polymer (GFRP) composite‐based FMLs. The synergetic effect of the two modification techniques resulted in high degrees of improvement in delamination resistance that were ~28% for critical strain energy release rate during mode‐I interlaminar fracture toughness (ILFT), that is (GIC) and ~37% for GIIC. Simultaneously, the flexural strength, tensile strength, and interlaminar shear strength improved by ~23%, ~17%, and ~24%, respectively. Scanning electron microscopy, atomic force microscopy, and surface energy measurement studies showed that the chemical pre‐treatment significantly influenced the surface morphology, surface roughness, and surface energy responses of aluminum, respectively. Fractographic study validated the effect of modification methods on the failure behavior under various testing modes.

Use of Random Forest to Predict Intermediate Temperature SCB Jc Parameter of Long-Term Aged Asphalt Mixtures

With the growing use of reclaimed asphalt pavement (RAP), recycled asphalt shingles (RAS), and other innovative additives in asphalt mixtures, there are concerns about the accuracy of Superpave volumetric-based mixture design. Performance tests in mix design procedures are needed to ensure desirable pavement performance. The Louisiana Department of Transportation and Development (LADOTD) has adopted the semi-circular bend (SCB) critical strain energy release rate parameter, Jc, to evaluate the cracking resistance of asphalt mixtures. To address practical shortcomings, this study aims to develop a predictive model to estimate SCB Jc at intermediate temperature of long-term aged (LTA) asphalt specimens from volumetric properties of plant-produced asphalt mixtures, and rheological and chemical properties of unaged asphalt binder by using a machine-learning model, random forest. Asphalt mixture SCB test and asphalt binder rheological and chemical properties tests were conducted. Stepwise correlation analysis was used to determine the most influential variables to SCB Jc. Random forest model was optimized using grid search with hyperparameter combinations. Results show that the developed random forest model was able to predict the SCB Jc fracture parameter of asphalt mixtures and a good agreement was observed between predicted and measured SCB Jc values. Variable importance scores based on mean decrease in impurity (MDI) showed that the Δ Tc had the most influence on SCB Jc prediction accuracy, and other inputs such as coarse aggregate type, LTA days, Fourier transform infrared spectroscopy test carbonyl index, and linear amplitude sweep test ALas also had significant effects on SCB Jc.

On the mixed mode I/II translaminar fracture of plain-weave carbon, E-glass and Kevlar reinforced laminated composites

The main aim of this study is to investigate the influence of long fiber types on the translaminar fracture behvior of epoxy-based composites subjected to pure mode I, mixed mode I/II and pure mode II using a combined experimental study and finite element (FE) analysis. Compact tension shear (CTS) test configuration was used to determine the critical strain energy release rate (CSERR) of the laminated composites reinforced with three types of high-performance fibers: Carbon, E-glass and Kevlar fiber. We believe that this is the first published report on the full combination of mode I, mixed mode I/II and mode II translaminar fracture toughness of laminated composites reinforced by three types of fiber. The translaminar fracture envelopes of the tested materials were illustrated. The results revealed that the translaminar CSERR of the composite systems is strongly dependent on the reinforcement type and the loading condition. The mode I translaminar CSERR of E-glass, Carbon and Kevlar fiber reinforced composites are equal to 16.87, 13.52, and 18.29 kJ/m2, respectively. Besides, under mode II loading condition, the translaminar CSERR of the laminated composites reinforced by E-glass, Carbon and Kevlar is obtained as 15.21, 7.82, and 8.45 kJ/m2, respectively. Fractographic analysis manifested that fiber pull-out clustering, fiber splitting, fiber breakage and matrix cracking are the main energy dissipating mechanisms happened on the fracture surface of the laminated composites.