Energy Release Rate Model Research Articles

Acoustic Emission Energy Release Rate Model for Classification of Damage Development in Large Fiber Reinforced Plastic Composite Structures

Acoustic emission identification of fracture mechanisms in composite materials is of great importance for the practical assessment of the serviceability of aerospace structures, such as unmanned aerial vehicles, rocket motors, and others. Many scientific research studies conducted in recent decades have demonstrated the unique capabilities of the Acoustic Emission (AE) method to detect and identify different failure mechanisms, including fiber breakage, matrix cracking, and delaminations in fracture tests of composite specimens. However, testing large composite structures, in many cases, can be accompanied by multiple time-overlapped fracture events activated simultaneously, resulting in considerable difficulties in the classification and assessment of combined prolonged AE signals. In this work, we propose the Energy Release Rate (ERR) model for the classification of AE activity related to fiber-reinforced plastic (FRP) composite fracture. The model identifies accurately both micro-scopic and macro-scopic fracture mechanisms in large aerospace structures having complex composition of materials. The model is practically applied using several machine learning methods and provides a simple means to identify and discriminate typical fracture mechanisms and their combinations. Specifically, we describe ERR model, the choice of most informative AE parameters, the choice of suitable machine learning classification methods, their training and testing on FRP specimens, and validating the model in practical tests of large full-size FRP composite structures.

Damage analysis of OC4 jacket subjected to cyclic loading by peridynamic approach

Catastrophic structural failure caused by fatigue damage under cyclic loads can be avoided by identifying critical locations of the damage initiation and the fatigue life during the design stage. Peridynamic (PD) theory defines structure as a collection of material points with non-local bond interactions where the structural discontinuity due to fatigue represented by instantaneous bond breakage is estimated through cumulative decrement of the bond’s life at each load cycle. In this work, we model a reference jacket presented under the Offshore Code Comparison Collaboration Continuation project (OC4) through peridynamic beam formulation. Initially, the static deformations of the beam and deformations of the OC4 jacket under static, harmonic, and irregular point loads are validated with ABAQUS results in all six degrees of freedom. Thereby, the PD fatigue parameters of the jacket’s steel material are calibrated from the experimental data of the corresponding material with a trial simulation for fatigue damage analysis. Later, different load cases from regular waves interacting with the jacket are generated in the PD framework by adopting linear wave theory. Based on the PD cyclic energy release rate model, a comparative study of all load cases to identify critical damage locations with the failure load cycles for damage initiation and fracture is performed for the considered OC4 jacket.

An investigation on fracture toughness predictions from mini-sized uniaxial tensile specimens with global and local approaches

This study provides investigations on whether the fracture toughness can be accurately predicted from mini-sized uniaxial tensile specimens with existing global and local approaches. The critical toughness model, based on classical fracture mechanics, and the energy release rate (ERR) model, based on damage mechanics, were used as the two representative global approaches. While the finite element simulated compact tension (CT) specimen implemented with Gurson-Tvergaard-Needleman model was used as the local approach. Specimen size effect was judged through the viewpoints of stress–strain relationship and damage development. It was proved that the specimen size has no significant influence on stress–strain relationship, and has little influence on damage developments when the thickness reaches 1.0 mm. Fracture toughness predictions were conducted on four metals, including two steels (SA508Gr.3Cl.1 and 18MnMoNbR), one aluminum alloy (6061-T651), and one titanium alloy (TC4). For TC4 exhibiting brittle cleavage features on the fracture surface of CT specimens, neither the global nor the local approach can accurately predict its fracture toughness. For 6061-T651 exhibiting both ductile and brittle features on the fracture surface of CT specimens, there exists significant macroscopic crack propagation at the moment of conventional fracture toughness determination. The existence of significant macroscopic crack is inconsistent with the “equivalent crack” assumption in the ERR model, leading to a failure in its fracture toughness prediction. For two steels following the “equivalent crack” assumption, the ERR model and the local approach yield more accurate predictions (with the maximum error around 10 %) than their critical toughness counterpart (with the maximum error around 30 %).

An experimental investigation on predicting the fracture toughness distributions in ferritic-austenitic stainless steel dissimilar metal welds from spherical indentation tests

This study provides an experimental investigation on predicting the fracture toughness distributions in dissimilar metal welds (DMWs) connecting the nozzle of reactor pressure vessel (made of low-alloy steel) and the safety end of pipes (made of stainless steel). Indentation energy to fracture model with three criteria (namely the critical stress, critical strain, and critical damage variable, CDV) and the energy release rate (ERR) model were introduced into fracture toughness predictions from spherical indentation tests (SITs). It was found that consistency of the fracture toughness KIC calculated from the repeated tests using the critical strain criterion and ERR model is even higher than that from mini-CTs, while high dispersion predictions were observed in critical stress criterion. Compared with the CDV criterion, the ERR model focuses on the dissipation energy required to form unit area “equivalent-crack” (i.e., the rate) rather than the whole indentation energy till a critical depth, and thus it is less affected by the absolute value of damage variations in three repeated SITs. Source of errors were first investigated through the damage developments in uniaxial tensile specimens manufactured from different zones of the DMWs, which proves the CDV varies from 0.1 to 0.25 and thus shall not be regarded as a constant. Then, SEM observations were conducted on both the fracture surfaces from mini-CTs and the section surfaces from SITs, indicating both the changes in fracture mechanism (from ductile dominated to the joint effort of ductile void developments and cleavage micro-crack propagations) and the existence of small initial voids from welding lead to the errors in damage-mechanics-based predictions.

A modified MERR model for predicting mode II fracture initiation angle considering boundary constraint effect

AbstractDuring the service process of brittle materials like marble, soda‐glass, and acrylic, mode II fracture is usually a typical failure mode. The fracture crack initiation, which is a critical factor affecting mode II fracture behavior, is an essential issue for understanding the fracture mechanism and determining fracture toughness. This paper proposed a modified maximum energy release rate model to predict the mode II fracture initiation angle through superimposing two idealized boundary conditions, remote loading, and crack‐face traction. The degree of the boundary constraint effect in finite‐size specimens was quantified by introducing the dimension‐ratio parameter. As experimentally validating through tension‐loading shear fracture tests of brittle poly(methyl methacrylate) (PMMA), the proposed model was demonstrated to be a good prediction of the mode II fracture initiation angle. The applicability of the proposed model was also verified with other brittle materials and fracture test techniques in references. The findings provide an insightful understanding of the mode II fracture behavior of brittle materials.

A Comprehensive Study of Fracture Toughness Determination from Conventional and Unconventional Methods

In this work fracture toughness is determined by the Toughness model; Critical Stress-Strain Model and Energy release rate model using unconventional test method referred to as Spherical Indentation test (SIT) to reduce the large and costly experimental set up as required in Conventional Fracture Toughness Test. The toughness model correlates the indentation energy to fracture with fracture toughness, Critical Stress-Strain Model assumes that the critical fracture toughness is equal to the critical plastic work done by the material when a crack tends to propagate and as per the Energy release rate model, indentation depth is given by loading-unloading cycles. The unloading slope which is elastic provides the reduced Young’s Modulus of the material from each unloading cycle which reflects the occurrence of damage in the material. For the determination of contact radius at different indentation points, finite element analysis is performed using the material data obtained from the tensile test result obtained from the previous work of the author. Conventional method using the Compact Tension (CT) and Three-Point Bending (TPB) specimens for the same material is used to determine the fracture toughness and compared with the above-described model.

A comparative study on fracture toughness calculation models in spherical indentation tests (SITs) for ductile metals

The study aimed to verify the effectiveness of fracture toughness calculation models in spherical indentation tests (SITs). Four representative models, the Haggag toughness (HT) model, critical indentation energy (CIE) model, critical stress-strain (CSS) model, and energy release rate (ERR) model, which were developed on different assumptions, were selected, and experiments were performed on 10 kinds of ductile metals. A comparison proved that none of the four models provide acceptable predictions for all experimental materials. The HT model provided the best fracture toughness KIC calculation for TC4, but failed for 6061 and some steels, while the other three models failed in predicting the KIC of TC4. The ERR model provided an overall acceptable prediction (with a maximum error around 20%, except for TC4) while the maximum errors in the other three models exceeded (or reached) 40% for steels and 6061. Errors were investigated from the effectiveness of empirical values used in each model, which proved that the stress ratio exhibits the best consistency and thus explained the reason why the ERR model provides the best fracture toughness calculations. The reason why the KIC of TC4 cannot be calculated with continuum-damage-mechanics based CIE and ERR models was also clarified through an investigation on its fracture (damage) mechanism through SEM observations. Further investigation proved that the fracture toughness can also be calculated from uniaxial tensile tests with an application of the CSS or ERR model, which verified the universality of these two models.

Effects of loading modes on reliability of cracked structures using FORM and MCS

Studying the reliability of cracked structures under different types of failure modes such as a mixture of Mode I and Mode II loadings has been of great importance in many applications. The purpose of this study is to evaluate the effects of different modes of loading, i.e. pure Mode I, pure Mode II and Mixed mode I/II loadings on the reliability of cracked structures via three typical case studies including 1st: through crack in a very wide plate, 2nd: cracked pressurized fuselage and 3rd: cracked fastener holes under actual geometries and loading conditions using the FORM, the fracture toughness and the equivalent SIF for Mixed mode I/II loading which is extracted by the Energy release rate model 1. The MCS was used to check the accuracy of the FORM. It was found that the failure probability decreases significantly as the loading mode changes from the pure Mode I to pure Mode II. This means that the reliability in the Mixed mode I/II loading is higher than that of pure Mode I and smaller than for pure Mode II. Also, it was concluded that the failure probability decreases with increasing of the angle of crack for the Mixed mode I/II loading conditions. The results indicated that the angle of crack and the applied stress are the two variables which have the most significant influence on the reliability.

Dielectric Breakdown Mechanism of Perovskite-Structured Ceramics

We precisely measured the dielectric breakdown strength of SrTiO3, CaTiO3, and CaZrO3 ceramics as a function of temperature, and revealed the dielectric breakdown mechanism of the ceramics. For the dielectric breakdown test, ceramics specimens with a lot of round-bottom holes were prepared. Using the specimens, the breakdown positions were stabilized and a reliability of breakdown strength was improved as well as the measurement efficiency. As a result of the dielectric breakdown tests, it was found that the dielectric breakdown strength decreased with increasing permittivity at room temperature and the permittivity dependence of breakdown strength obeyed Griffith type energy release rate model. At high temperature above 100ºC, the dielectric breakdown mechanism of SrTiO3 and CaTiO3 ceramics was explained by an intrinsic breakdown model. In contrast, an intrinsic dielectric breakdown of CaZrO3 ceramics didn't occur in the measurement temperature range up to 210ºC. To obtain a high dielectric breakdown strength at high temperature, the dielectric permittivity is required to be low to some extent and the defect concentration of oxygen vacancies should be minimized in the perovskite-structured oxide.

A Griffith type energy release rate model for dielectric breakdown under space charge limited conductivity

An energy release rate based “fracture” model is presented, which is able to describe unstable dielectric breakdown of ceramic and polymer insulators. The electric field and electrostatic energy of an electrically conducting filament within a spheroidal surface electrode is calculated. As space charge injection is allowed the electric field singularity at the electrical conducting filament is reduced. As a consequence it is possible to solve the electrostatic problem even for filaments where the diameter is reduced to zero and the energy release rate can be formulated only as a function of the filament length. The presented energy release rate together with the formulation of a dielectric breakdown criterion allows understanding the experimentally measured one over square root sample thickness dependence and the pronounced scatter of the measured dielectric breakdown strength.

Scaling of First-Ply Failure and Strength in [+ϑn/−ϑ/−ϑn/90/902n]s Laminates: Experiments and Predictions

An experimental investigation of first-ply failure and strength was conducted on ply-level scaled carbon/epoxy composite laminates having a stacking sequence of [+ϑn/−ϑ/−ϑn/90/902n]s where the constraint ply angle, ϑ, was varied from 0 to 75°, and where the constraint ply angle, ϑ, was varied from 0 to 75°, and n varied from 1 to 4. First-ply failure was shown to depend on the level of constraint and the scale factor, n. The strain energy release rate for matrix microcracking was computed from first-ply failure data of the [02/902]s laminate. Then, first-ply failure for all other layups was predicted using a numerical model that accounted for both constraint and size. Tensile strength was predicted using a strain energy release rate model for delamination of surface angle plies. A delamination energy value for each ply angle was calculated from the thinnest (n = 1) laminates to predict strength of the other sizes.

Analytical and experimental methods for a fracture mechanics interpretation of the microbond test including the effects of friction and thermal stresses

An energy release rate model based on a generalized fracture mechanics of composites was developed for analyzing the microbond test. This model, which extended a previous model, includes both friction at the fiber/matrix interface and residual thermal stresses. A series of microbond tests on macroscopic specimens were carried out for evaluating the model. In some specimens we could observe debond crack growth. These results could be interpreted with a fracture mechanics R-curve which led to a measured interfacial fracture toughness. In many specimens, debond crack growth could not be observed. We developed an approximate method for determining interfacial fracture toughness even without knowledge of debond crack size. The macroscopic specimens were designed for studying the optimal approach to analysis of microbond specimens. The geometry of the macroscopic specimens, however, could also be used to measure the mode II toughness of adhesive bonds.

Effect of temperature on the transverse cracking behavior of cross-ply composite laminates

Abstract This paper investigates temperature-dependent transverse cracking in cross-ply composite laminates over a wide range of service temperatures. The graphite-reinforced polymer-matrix composites considered are bismaleimide X5260/G40-800 (BASF) and Avimid K3B/IM7 (DuPont) materials. Fracture toughness is measured over a range of temperatures from − 50°C to 175°C and is found to be temperature dependent. Matrix cracking initiation is quantified experimentally using acoustic emission polar backscattering, ultrasonic inspection, and edge replication. Various modeling approaches are correlated with experimental results. It is found that the shearlag model and the energy release rate model provide upper and lower bounds on experimental results. The significance of including temperature-dependent properties is demonstrated.

Buckling and postbuckling behavior of delaminated sandwich beams

An investigation was performed to study the buckling and postbuckling behavior of sandwich beams containing lengthwise and depthwise through-the-width delaminations. An analytical beam model was developed to predict the buckling load of the beam and to describe its postbuckling response for arbitrarily situated delaminations and various combinations of boundary conditions. Griffith's energy release rate model was employed to predict the stability of delamination propagation under external loading and to determine the direction of delamination growth. Parametric studies over a wide range of beam geometries, damage sizes and locations, composite facings and beam boundary conditions were carried out to study their effects on the overall behavior of the sandwich structure, as well as its damage tolerance. The results demonstrated that a sandwich construction is very ‘sensitive’ to the presence of delaminations situated at the core-faceplate interface. Premature buckling failure occurs at external loads which are significantly lower than the buckling load for a ‘perfect’ sandwich beam; in ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load-carrying capacity of the beam; varying either the boundary conditions in a sandwich beam or the lengthwise location of a delamination has a small effect on the postbuckling behavior of the beam. Delaminations located within composite faceplates have less pronounced influence, and as the defect is moved outwards the limit load may reach the buckling load corresponding to that of the ‘perfect’ beam. The proposed model is capable of analyzing the postbuckling behavior of both sandwich and composite laminated beams for arbitrary locations of the delamination, and various combinations of boundary conditions.

Influence of predetermined delaminations on buckling and postbuckling behavior of composite sandwich beams

An investigation was performed to obtain the behavior of composite sandwich beams in the presence of predetermined delaminations, due to disbonding between the faceplate and the less rigid core. An analytical model for predicting buckling and describing the postbuckling behavior of the beam was developed. Griffith's fracture energy release rate model was introduced to predict the stability of the delamination propagation under external loading. Parametric studies over a wide range of damage sizes, and composite facings were carried out to study the effects of these parameters on the overall behavior of the beams, as well as its damage tolerance. The results demonstrate that sandwich construction is very ‘sensitive’ to the presence of predetermined delaminatoins: premature buckling failure occurs at external loads, which are significantly lower than those corresponding to a ‘perfect’ sandwich beam. The limit load is obtained before delamination propagation takes place. In ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load carrying capacity of the beam. It was also shown that the proposed model can be used to study the influences of predetermined delaminations in composite beams.

Characterization of delamination resistance in composite laminates

One approach to obtaining more damage tolerant laminated composite structures can be achieved by improving the properties of the composite material itself. This approach needs full knowledge of resistance to typical damage modes which appear to affect the use of structural composite laminates. In this work, a representative model for delamination growth in composite laminates is presented, and a simple energy release rate model for delamination growth is established. Emphasis is placed on discussing the characteristics of delamination resistance in T300/648 and T300/634 graphite/epoxy composite laminates. The results indicate that the laminated composite structures with more laminate resistance to delamination growth can be obtained by improving the ductility of matrix resin.

Role of matrix resin in delamination onset and growth in composite laminates

The effect of the matrix resin on the onset and growth of delamination in composite laminates has been investigated in this work. Two kinds of graphite/epoxy composite materials (T300/648-BF 3/MEA and T300/634-DDS) with quite different matrix properties have been used. The study was done on two different layups, [(±30) 3/90 2] s and [(±45) 2/O 2/90 2] s . Out-of-plane moiré interferometry and diiodomethane-enhanced X-radiography were used to detect delamination. A strength criterion for the onset of delaminatoin is proposed and an assessment made of the effect of matrix properties on delamination onset. A modified energy release rate model is presented for characterization of delamination growth emphasis being placed on assessing the behavior of delamination resistance curves and delamination growth rate. The results indicate that enhancement of matrix strength and ductility increases the critical loads for delamination onset and delamination resistance in the composite laminates under static loading, and significantly reduces the delamination growth rate under cyclic loading.