Strength-based Failure Research Articles

The influence of microstructure on the tensile properties of a creped tissue paper: Modeling and experiments

Low density tissue papers are soft fiber networks with a folded internal microstructure—deliberately imparted during a widely used manufacturing process, called dry creping. The folded crepe structure enhances a tissue paper’s specific volume, stretchability, and softness. The influence of the micron-scale crepe structure on nonlinear tensile response is studied using experiments and a discrete elasto-plastic model (DEM). First, ‘Crepe Index (CI)’ is defined to quantify the crepe structure. An optical method to obtain high resolution edge images is developed to measure the CI. The relationship between the CI and tensile failure strain and initial elastic stiffness is assessed: the failure strain is observed to be proportional to CI, while the dependence of initial stiffness on CI is unclear–presumably due to the damage induced through the de-densification of fiber layers during the manufacturing. The effect of CI on initial stiffness and failure strain is assessed using DEM by idealizing the creped paper as a segmented triangular wave—each segment governed by a bilinear elastoplastic constitutive law and a strength-based failure criterion. The model reveals that the initial stiffness of a creped sheet depends not only on the CI but also on sheet-thickness to crepe-wavelength ratio, and the stiffness of the uncreped sheet. The failure strain is found to be stretching dominated at low CI, and bending dominated at higher CI. Qualitative agreement is found between the DEM and experiments. The significance of both the material and the geometric non-linearity on the macroscale tensile response of a creped tissue paper emerges from this study.

Influence of loading orientation on mechanical properties of spot welds

The mechanical performance and failure characteristics of resistance spot welds from two grades of third-generation advanced high strength steels (3G-AHSS), designated 3G-980 and 3G-1180, to combined/mixed loading were investigated by conducting KS-II tests in eight different loading orientations. Due to inherent difficulty in gripping the high strength 3G-AHSS, a combination of coupon rotation, slippage, and deformation occurred especially at shear-dominated loading orientations. This study utilized a new fixture based on Arcan-apparatus coupled with digital image correlation technique to track the instantaneous orientation of the KS-II coupons. This way, the actual proportion of shear and tensile components of force applied to the nugget, instead of the nominal ratio at the beginning of the tests, could be quantified experimentally, which in turn improved the calibration accuracy of a spot weld strength-based failure criterion. A novel triangulation method was proposed to minimize the influence of coupon slippage and deformation at regions away from the nugget on calculated absorbed energy. The more precise absorbed energy calculation was achieved by changing the displacement reference point from the crosshead to a local measurement between coupon halves. Energy absorption capabilities of the spot welds were calculated by separately tracking the deformation of the nugget in the shear and tensile directions. It was observed that within the tensile-dominated loading orientations (45°–90°) pullout failures of 3G-980 spot welds exhibit much higher post-failure energy absorption capabilities than the RSW of 3G-1180. The propagation of the formed cracks into the fusion zone was found responsible for the relatively inferior energy absorption capability of 3G-1180 joints.

Structural Analysis and Optimization of Wings Subjected to Dynamic Loads

Dynamic loads arising from the Title 14 Code of Federal Regulations (14 CFR; “Aeronautics and Space,” Federal Aviation Administration, U.S. Dept. of Transportation, Subchapter C Aircraft, Part 25 Airworthiness Standards: Transport Category Airplanes, https://ecfr.federalregister.gov/current/title-14/chapter-I/subchapter-C/part-25 [retrieved 23 August 2021]) are critical drivers of aircraft design. The aircraft structural design process is an iterative one involving computationally expensive simulations. Existing methods simplify the dynamic loads to equivalent static ones and design the structure using shell-based analysis. Other literature approaches use beam models for structural sizing but make assumptions on the geometry, material distribution, or both. In this work, the use of the Variational Asymptotic Method is explored to 1) systematically reduce the three-dimensional (3-D) wingbox to a one-dimensional (1-D) model, 2) solve the 1-D model using a nonlinear beam theory, and 3) recover the stress field on the wingbox. An adjoint-driven gradient-based structural optimization framework is developed to size the structure for dynamic loads subjected to strength-based failure considerations. The proposed structural analysis method is applied to the wingbox structural analysis and sizing of a novel hybrid-electric propulsion aircraft: NASA’s Parallel Electric-Gas Architecture with Synergistic Utilization Scheme (PEGASUS) concept. Results in the paper show that the sizing of aircraft wings for 14 CFR specified maneuvers 2.5 and static maneuvers using the proposed approach produces a 6% difference in weight compared to a shell-based method but with a speedup of 7.8 times, and it is efficient at sizing the wingbox structure for dynamic loads generated by gust maneuvers.

Fracture angle prediction for matrix failure of carbon-fiber-reinforced polymer using energy method

In this study, an energy-based model for predicting the fracture angle of matrix failure in unidirectional carbon-fiber-reinforced polymer (CFRP) under three-dimensional mechanical loading was developed. The elastic stresses in the undamaged area and the frictional stresses in the damaged area were considered in determining the complementary free energy density in the CFRP damage process. The fracture angle of the transverse matrix failure was predicted based on the maximum dissipation rate of the energy density. The effect of the stress state in the damaged area on the energy density was analyzed under the matrix tension and compression failure modes. The predicted fracture angle was verified by comparison with existing strength-based matrix failure criteria under various stress conditions. The computational efficiency between the energy-based and strength-based failure criteria is compared and evaluated.

NONLOCAL CONTINUUM ADAPTIVE ELASTIC BONE-COLUMN BUCKLING MODEL

It is well argued that stability-initiated failure dominates, especially in older bone, because of the instability of single trabeculae which is prone to inelastic buckling at stresses far less than expected for strength-based failure. It is also well known that when several horizontal struts have disappeared, trabecula fails due to compression-buckling load. In this contribution, our main goal is to improve, from theoretical point of view, the mechanistic understanding of bone buckling failure which is known to be at the core of important clinical problems. For that and with respect to previous works, an attempt is made in order to establish a simplified adaptive-beam buckling model, formulated within the context of the nonlocal adaptive continuum mechanics, from which numerical computations were performed in order to get a better knowledge about bone-column buckling mechanism affected by both bone density and bone density gradient distributions restricted to Euler–Bernoulli beam theory. An attempt is made to compare the experimental data with the response of our simplified model. For that, controlled buckling tests of single trabeculae were carried out from three medial tibia end sections (knee joint).

Yield stress criteria to assess the buildability of 3D concrete printing

3D concrete printing (3DCP) using the extrusion method is a commonly used additive manufacturing technique to construct the structures layer by layer without using formwork. Therefore, the green (wet or fresh) strength of the printable concrete determines the possible printable height of the structure and the rate of printing to avoid collapse during the printing process. This paper aims to identify the buildability criteria based on the green strength of concrete and the effect of early age material properties on the stability of printed structures. The commonly available strength-based failure models based on the material yield stress and the vertical stresses induced were developed considering higher aspect ratios (height to width ratio). This may be not suitable for lower aspect ratios used in 3DCP layer geometries. Also, the frictional behaviour due to the applied vertical stresses should be considered in the material used for 3DCP applications. In this work, the Mohr-Coulomb based buildability criterion was developed and validated with laboratory experiments and numerical simulations. The laboratory experiments were carried out to establish the time-dependent material and rheological properties of 3D printable concrete mixes. Further, 3D printing of hollow circular sections was carried out to study the failure modes and to obtain the build height at the time of failure. The nonlinear finite difference model of the 3D printed sections was developed with the user-defined time-dependent material models to assess the accuracy of the proposed buildability criterion. Additionally, the proposed buildability criterion was further validated with the 3DCP experimental and numerical data presented in literature and all confirm that the proposed criterion shows higher accuracy over existing methods in assessing the buildability.

A criterion-selection diagram for the thermal shock resistance of a hollow circular cylinder

The characteristics of thermally induced failure are investigated for a hollow circular cylinder exposed to a convective cooling at the inner surface. The transient fields of both temperature and thermal stresses are given in closed forms over the full range of Biot number. The thermal shock resistance (TSR) is analyzed based on two distinct failure criteria. Namely, the strength-based failure criterion is adopted for a nearly flaw-free cylinder while the fracture toughness-based one is used for the counterpart with an inner crack-like flaw. From each criterion, the admissible maximum temperature drop is obtained assuring that a hollow cylinder can tolerate without failure. The influence of flaw size on the TSR is quantified and a criterion-selection diagram is proposed for the TSR characterization. These results are deemed to be of importance from the perspective of estimating the TSR of a hollow circular cylinder.

On power-law tail distribution of strength statistics of brittle and quasibrittle structures

Understanding the tail behavior of the probability distribution of structural strength is of paramount importance for reliability-based design of engineering structures. For brittle and quasibrittle structures, the tail distribution not only determines the design strength at a low failure probability, but also governs the functional form of the strength distribution of large-size structures. There exists clear evidence that the Weibull distribution is applicable to brittle structures. Based on the theory of extreme value statistics, the applicability of Weibull distribution suggests that the tail distribution must follow a power law. The justification of the power-law tail distribution was first proposed by Freudenthal based on an assumed type of flaw statistics and linear elastic fracture mechanics of non-interacting flaws. A series of recent studies suggested that the power-law tail can be explained by the transition rate theory governing the statistics of material failure at the nano-scale. In this study, we investigate the tail distribution by considering the randomness in both material strength and applied stress field. The present analysis adopts a nonlocal strength-based failure criterion, in which the spatial variability of the material strength is represented by an autocorrelated random field. The failure statistics of the structure is calculated as a first passage probability. We analyze this problem in 1D, 2D and 3D settings, and the results indicate that in all cases the tail distribution of the nominal structural strength follows a power law. It is shown that the power-law tail behavior of strength distribution stems from the tail distribution of material strength. The flaw statistics introduces additional randomness to the nominal structural strength, but does not dictate the power-law form of its tail distribution.

The influence of skin-core residual stress and cooling rate on the impact response of carbon fibre/polyphenylenesulphide

This study investigates the influence of macroscale skin-core residual stress and cooling rate on the impact response of aerospace grade carbon fibre/polyphenylenesulphide (CF/PPS). Numerical simulations are developed which analyse the thermal shrinkage and residual stress development of unidirectional (UD) lay-up configurations. Macroscale skin-core residual stresses are then incorporated into low-velocity impact simulations based on an orthotropic elastic material model. Interlaminar delamination is modelled using a bilinear cohesive traction–separation law, and intralaminar failure is modelled using the Chang–Chang strength-based failure criterion. The simulation results are compared with the results of drop tower impact tests showing qualitative agreement in terms of maximum impact force and delamination. The results of this work highlight the importance of cooling rate on the interlaminar delamination and intralaminar failure of CF/PPS.

Mechanical behavior of the composite curved laminates in practical applications

In order to determine the mechanical behavior of the curved laminates in practical applications, three right-angled composite brackets with different lay-ups were investigated both experimentally and numerically. In the experimental, quasi-static tests on both unidirectional and multidirectional curved composite brackets were conducted to study the progressive failure and failure modes of the curved laminates. In the numerical modeling, three-dimensional finite element analysis was used to simulate the mechanical behavior of the laminates. Here, a strength-based failure criterion, namely the Ye criterion, was used to predict the delamination failure in the composite curved laminates. The mechanical responses of the laminate subjected to off-axis tensile loading were analyzed, which include the progressive failure, the failure locations, the load-displacement relationships, the load-strain relationships, and the stress distribution around the curved region of the angled bracket. Subsequently, the effects of stacking sequence and thickness on the load carrying capacity and the stiffness of the laminates were discussed in detail. Through the experimental observation and analysis, it was found that the failure mode of all the specimens is delamination, which is initiated abruptly and develops unstably on the symmetric plane, close to the inner surface, and about along the circumferential direction. It was also found that the stacking sequence and the thickness have significant influences on both the load carrying capacity and the stiffness of the laminates. However, the thickness effect is less than that on the curved aluminum plate.

Elastic bone-column buckling including bone density gradient effect within the context of adaptive elasticity

ObjectivesOur main goal is to improve, from theoretical point of view, the mechanistic understanding of bone buckling failure which is known as at the core of important clinical problems such as osteoporosis. Material and methodsWhat is well argued is that in older bone, stability-initiated failure dominates because of the instability of the individual trabeculae which is prone to inelastic buckling at stresses far less than expected for strength-based failure. Taking advantage of our previous work, an improved original Euler's adaptive-beam buckling equation incorporating density gradient effect is investigated. ResultsFor one, we indicate that resorption can leads to new elastic instabilities that can conduct to bone-buckling mechanism of fracture. For another, we demonstrate that bone density gradient play a key role in the initiation of the bone-column elastic buckling instability. ConclusionAs a result, it is clearly stated here that firstly, the number of these elastic instabilities which are potentially implied in the mechanisms of bone fracture, localized at the trabecular element scale, depends strongly upon the material parameter η and secondly; the bone density gradient affect notably the stability of the bone-column deflection.

Griffith criterion for brittle fracture in graphene.

There are prevailing concerns with the critical dimensions when conventional theories break down. Here we find that the Griffith criterion remains valid for cracks down to 10 nm but overestimates the strength of shorter cracks. We observe the preferred crack extension along the zigzag edge in graphene, and explain this phenomenon by local strength-based failure rather than energy-based Griffith criterion. These results provide a mechanistic basis for reliable applications of graphene in miniaturized devices and nanocomposites.

Strength prediction of bolted joints in CFRP composite laminates using cohesive zone elements

A strength prediction method is developed for bolted joints in CFRP composite laminates using cohesive zone elements (CZEs). Three-dimensional finite element models were developed with one element per laminate layer using the ANSYS software (ANSYS, 2009) [1]. CZEs were embedded into the subcritical (matrix based) damage locations that were determined from the X-ray radiographs as detailed in Atas and Soutis (2013) [2]. CZEs use a strength-based failure criterion to predict the onset of damage and a fracture mechanics based approach to predict its growth. The material properties required to simulate the subcritical damage modes were the interfacial strength, fracture energies and the nonlinear shear stress–strain behaviour of the particular material system used. The strength of the joints was determined through the load–displacement curves of the cross-ply laminates and by a simple maximum stress criterion for the quasi-isotropic specimens. It has been shown that the effect of various joint geometries and laminate lay-ups on the joint strength was accounted for by the method developed.

Failure of Composites with Short Fibers

Strength-based failure criteria are commonly used with the finite element method (FEM) to predict failure events in composite structures. The laminate analogy is very useful for the calculation of the strength of composite materials with short fibers. The prediction of the laminate strength is carried out by evaluating the stress state within each layer of the laminate based on the classical lamination theory. In this paper FEM is used as a tool to predict the laminate strength. Failure criteria are used to calculate a failure index (FI) from the computed stresses and user-supplied material strengths. The micromechanical analysis has been carried out using computer package MATLAB and numerical simulation has been executed by using a commercially available ANSYS code.

Structural Performance of FRP Composites in Fire

This paper reviews the experimental and modeling work that has been carried out concerning the behavior of fiber-reinforced polymer (FRP) composites in fire since the 1980s. The first part focuses on the thermophysical properties and temperature responses, while the second considers thermomechanical properties and responses, which are significantly affected by the thermal exposure of the FRP material. Furthermore, the application of deformation-based or strength-based failure criteria enables the prediction of time-to-failure. If the fire exposure time is less than the time-to-failure, the post-fire behavior is of interest and the post-fire properties and their potential recovery after cooling are particularly addressed. This fundamental understanding obtained as a result of both modeling and experimental work makes a reliable endurance design for FRP structures in fire possible.

Elliptical inhomogeneity in orthotropic composite materials due to uniform eigenstrains

Analytic solutions are presented for elastic fields induced by normal and shear eigenstrains in an elliptical region (inhomogeneity) embedded in orthotropic composite materials (matrix). Conformal transformation and complex function method are adopted to obtain exact stress distributions in the matrix at the interior boundary to calculate strain energy in the matrix. The stress fields in the elliptical inhomogeneity are derived analytically based on application of the principle of minimum strain energy of the elastic system to determine two fundamental variables characterizing the equilibrium boundary. The resulting solutions are verified with the continuity conditions for the normal and shear stresses along the interior boundary of the matrix. These reduce to known results for some special cases. Numerical examples are provided to illustrate the resulting solutions to the analysis of stress distribution pattern, strength-based failure and fracture behavior. The proposed model can be applied to evaluate volumetric expansion induced cracking and failure of polymers and polymer composites due to freezing of trapped moisture in the elliptical inhomogeneity region as well as fatigue strength of the materials under freeze–thaw conditions.

A multi-scale method to investigate delamination in electronic packages

Interfacial delamination, due to the presence of dissimilar material systems, is one of the primary concerns in an electronic package design. A number of failure criteria have been proposed to solve delamination problems with a pre-defined crack at the interface. However, in a predictive simulation of electronic package reliability, it is difficult to assign pre-defined cracks to a specific interface and to use such model as an effective vehicle in the performance evaluation of electronic packages. The present study is focused on the delamination at the epoxy molding compound (EMC)/Cu interface. A multi-scale model was built to determine the interfacial strain energy density between the EMC and copper substrate. The concept of virtual internal bond (VIB) approach was introduced to complement the interfacial layer model by providing a methodology to evaluate the interfacial material properties. The interfacial material properties were derived from atomic force microscopy (AFM) measurements using the Lennard–Jones potential. The interfacial material properties were assigned to the EMC/Cu interface to represent the interaction of the EMC with copper. The calculated interfacial strain energy density was incorporated into a strength-based failure criterion for interfacial delamination initiation.

Use of mode-I cohesive-zone models to describe the fracture of an adhesively-bonded polymer-matrix composite

In this paper, the use of a cohesive-zone approach to model the mode-I fracture of adhesive joints made from a polymer-matrix composite is demonstrated. Cohesive-zone parameters were obtained by matching numerical results to experimental observations. It is shown that there is a distinction between the characteristic strength of the interface associated with the toughness, and the intrinsic cohesive strength of the interface. While the characteristic strength and toughness are often sufficient to describe fracture in the presence of a crack, the intrinsic cohesive strength is also required to analyze some geometries that have very small characteristic dimensions or crack lengths. It is shown that cohesive-zone models accurately predict the behavior of the joints studied. In particular, not only are the strengths and deformations accurately described, but the transition between failure of the composite and failure of the interface can also be predicted. This mode-I transition cannot be predicted by conventional fracture mechanics as it depends on both the energy-based and strength-based failure parameters associated with cohesive-zone models.

Structural analysis of GRP pipe couplers by using a fracture mechanical approach

A three-dimensional (3D) finite element analysis on a newly developed type of coupler for glass-fibre-reinforced plastic (GRP) pipes under an internal pressure loading is presented. The stress distribution within the coupler is inhomogeneous with apparent stress concentrations located at the pipe and the coupler edges. Delamination and debonding are the main failure modes. Therefore, a fracture mechanical approach is preferred in the design of the coupler instead of a purely strength-based failure criterion evaluation. The strain-energy release rates evaluated at the critical delamination sites are used as a performance measure of the coupler. A comparative parametric study is carried out to allow for the dimensioning and shaping of the coupler as well as for the choice of an optimal stacking sequence.