Fracture limit prediction for roller hemming of aluminum alloy sheet

Roller hemming limit is predicted based on ductile fracture criterion in this approach. Plastic deformation in sheets made of aluminum alloy 6061-T6 is studied experimentally. Combined isotropic and kinematic hardening rule is considered in roller hemming numerical analysis. Forming limit stress curve at fracture (FLSCF) is derived from Cockcroft–Latham ductile damage criterion to determine fracture during roller hemming simulation. Serrated strain paths are detected along hemline. The zones where fracture takes place obtained by experiments and FE simulations are compared. It is demonstrated that FLSCF, which is on the basis of ductile damage criteria and basically irrelevant to linearity of strain path could be used to predict fracture of roller hemming correctly.     

Statistical comparison of two fracture criteria

Two fracture criteria are compared within the stochastic model of brittle fracture of a component with the random ensemble of crack-like defects.

The component comprises a random array of internal defects, represented by equivalent cracks. Under assumption of stochastic independence of defects and Poisson distribution of defects population the probability of fracture is determined. This probability is dependent on local fracture criterion applied to an arbitrary crack. The maximum normal stress and energy release rate criteria were applied to check as to whether they may yield significantly different prediction of above probability.

Computer calculations show that with the increase of defects density the difference in predictions of above two criteria became unsignificant and for both limiting fracture-stress curves converges to maximum stress theory. For low densities energy release rate criterion yields more conservative predictions in almost all range of λ. The limiting fracture-stress curves deviate in this case from both the maximum stress and von Mises theories.     

Strain-rate-dependent failure criteria for composites

The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10⁻⁴, 1 and 180-400 s⁻¹, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress-strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, and failure mode based and partially interactive criteria (Hashin-Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.     

混凝土I型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

Crack onset and propagation at fibre–matrix elastic interfaces under biaxial loading using finite fracture mechanics

A new fracture criterion able to predict crack onset and propagation at interfaces between solids is formulated, implemented in a computational code and applied to a particular problem in composites on a microscale. More specifically, this criterion is used to study the debond onset and propagation in mixed mode in the case of a single fibre subjected to a biaxial remote loading. The fracture criterion formulation is based on the Linear Elastic-(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Each of these criteria is a necessary but not sufficient condition for crack onset and propagation. Two empirical mixed-mode fracture criteria are considered and tested: the interface fracture toughness law by Hutchinson and Suo and the quadratic stress criterion. The FFM + LEBIM approach developed offers an adequate characterization of the interface stiffness in contrast to the too restrictive, original LEBIM formulation.     

Carbon nanofibers enhance the fracture toughness and fatigue performance of a structural epoxy system

This study investigates the monotonic and dynamic fracture characteristics of a discontinuous fiber reinforced polymer matrix. Specifically, small amounts (0-1 wt.%) of a helical-ribbon carbon nanofiber (CNF) were added to an amine cured epoxy system. The resulting nanocomposites were tested to failure in two modes of testing; Mode I fracture toughness and constant amplitude of stress tension-tension fatigue. Fracture toughness testing revealed that adding 0.5 and 1.0 wt.% CNFs to the epoxy matrix enhanced the resistance to fracture by 66% and 78%, respectively. Fatigue testing at 20 MPa peak stress showed a median increase in fatigue life of 180% and 365% over the control by the addition of 0.5 and 1.0 wt.% CNF, respectively. These results clearly demonstrate the addition of small weight fractions of CNFs to significantly enhance the monotonic fracture behavior and long-term fatigue performance of this polymer. A discussion is presented linking the two behaviors indicating their interdependence and reliance upon the stress intensity factor, K.     

Determination of critical strain for initiation of dynamic recrystallization

Using the work hardening rate–strain curves, an effective mathematical model has been developed to predict the stress–strain curves of alloy steel during hot deformation up to the peak stress regardless of the level of the strain, weather smaller or larger than the critical strain. This model is expressed in terms of peak stress, peak strain and one temperature-sensitive parameter, S. In addition, one new model, which is a function of peak strain, was proposed to predict the critical strain for the initiation of dynamic recrystallization using the second derivative of work hardening rate with respect to stress. Besides the theoretical study, the analysis is used to determine the stress–strain curves and critical strain of 304 austenitic stainless steel. The predicted results were found to be in accord with the experimental data.     

Determining the mechanism controlling glass fibre strength loss during thermal recycling of waste composites

This paper presents an experimental investigation into the large reductions to the tensile fracture stress and the associated strength loss mechanism of E-glass fibres during thermal recycling. Fractographic analysis reveals the fracture process is controlled by surface flaws, irrespective of heat treatment temperature and duration. The fracture toughness is an important material property in order to understand possible changes in the strength–flaw relationship during heat treatment. Focussed ion beam (FIB) milling is used to artificially create a single nano-sized deep notch (between 30 and 1000 nm) in glass fibres. The strength loss, fracture toughness, fracture mirror constant and fracture mechanism observed for nano-notched and thermally recycled fibres are identical, indicating bulk property changes do not occur during thermal recycling. The study proves conclusively that surface flaw growth is the controlling mechanism reducing fibreglass strength during thermal recycling of waste polymer composites.     

Fracture of austenitic steel subject to a wide range of stress triaxiality ratios and crack deformation modes

The stress triaxiality ratio (hydrostatic pressure divided by von Mises equivalent stress) strongly affects the fracture behaviour of materials. Various fracture criteria take this effect into consideration in their effort to predict failure. The dependency of the fracture locus on the stress triaxiality ratio has to be investigated in order to evaluate these criteria and improve the understanding of ductile fracture.This was done by comparing the experimental results of austenitic steel specimens with a strong variation in their stress triaxiality ratios. The specimens had cracks with varying depths and crack tip deformation modes; tension, in-plane shear, and out-of-plane shear. The crack growth in fracture mechanics specimens was compared with the failure of standard testing specimens for tension, upsetting and torsion. By associating the experimental results with finite element simulations it was possible to compare the critical plastic equivalent strain and stress triaxiality ratio values at fracture. In the investigated triaxiality regime an exponential dependency of the fracture locus on the stress triaxiality ratio was found.     

Fracture behaviour of plain and fiber-reinforced concrete with different water content under mixed mode loading

In the present paper, plain concrete and fiber-reinforced concrete are considered from the point of view of the mechanical characteristics, with particular emphasis on the fracture resistance, for different values of the water/cement ratio and different amount and type (metallic or polymeric) of reinforcing fibers. The main mechanical characteristics (such as compressive strength and tensile strength) of the examined materials have experimentally been determined, and several pre-cracked specimens have been tested under three-point bending up to the final failure in order to study the fracture behaviour by also evaluating the fracture energy. Furthermore, the crack paths for static tests under displacement control have been obtained, and the load–displacement deflection curves have been determined for different crack configurations. Assuming the fracture surface characterised by a fractal dimension, some quantitative evaluations of the fracture energy are carried out. Then, the fracture behaviour and the post-peak behaviour of plain and fiber-reinforced specimens are discussed, and the effects of reinforcing fibers are quantified. Some conclusions are finally drawn.     

Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension

The presence of stress concentrations at holes and notches is known to reduce the strength of composite materials. Due to complexity of the damage processes at a stress raiser in a composite, different modeling approaches have been developed, ranging from empirical point and average stress criteria to involved damage mechanics or cohesive zone-based models of failure. Finite fracture mechanics approach with a coupled stress and energy failure criterion, recently developed and applied mainly to cracking in homogeneous isotropic materials, allows predicting the appearance and propagation of a crack using material strength and toughness characteristics obtained from independent tests. The present study concerns application of the finite fracture mechanics to the analysis of cracking at a notch in a UD glass/epoxy composite subjected to tensile off-axis loading. Based on UD composite strength and intralaminar toughness characterized by separate tests, finite fracture mechanics analysis provided conservative estimates of crack onset stress at the notch.     

Microstructural and mechanical characteristics of PHEMA-based nanofibre-reinforced hydrogel under compression

Natural network-structured hydrogels (e.g. bacterial cellulose (BC)) can be synthesised with specific artificial hydrogels (e.g. poly(2-hydroxyethyl methacrylate) (PHEMA)) to form a tougher and stronger nanofibre-reinforced composite hydrogel, which possesses micro- and nano-porous structure. These synthetic hydrogels exhibit a number of advantages for biomedical applications, such as good biocompatibility and better permeability for molecules to pass through. In this paper, the mechanical properties of this nanofibre-reinforced hydrogel containing BC and PHEMA have been characterised in terms of their tangent modulus and fracture stress/strain by uniaxial compressive testing. Numerical simulations based on Mooney-Rivlin hyperelastic theory are also conducted to understand the internal stress distribution and possible failure of the nanofibre-reinforced hydrogel under compression. By comparing the mechanical characteristics of BC, PHEMA, and PHEMA-based nanofibre reinforced hydrogel (BC-PHEMA) under the compression, it is possible to develop a suitable scaffold for tissue engineering on the basis of fundamental understanding of mechanical and fracture behaviours of nanofibre-reinforced hydrogels.     

Optimisation of steel–composite connections for structural marine applications

Parametric variation and optimisation using genetic algorithms employing single and multi-objective functions are proposed for the optimisation of a structural steel/composite connection. The joint in marine applications is the connection between the steel hull and the composite superstructure of a naval vessel. A baseline joint is defined and all parametric variations and optimised joints are compared to this. The parametric results provided design curves of the joint performance determined from the weight, Von Mises stress in the adhesive and the global stiffness indicating performance sensitivity to specific changes in the joint geometry.

The results indicated that the parametric variations can lead to an improvement in the performance but high levels of human interaction are required to make a combined improvement to the performance. The use of genetic algorithms provided an efficient method of searching the design space for an optimal joint. The single objective function provides an excellent reduction in the weight and maintaining or improving the performance of the joint to in-plane compressive loading. The use of the multi-objective function whereby a weighting was applied to the weight, stress and stiffness performance criteria proved extremely successful in further optimising the joint. The use of genetic algorithms has been demonstrated to efficiently search the complex design space of a structural connection and the use of multi-objective functions as the most effective selection method.     

A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials

In engineering applications, it is difficult to avoid the non-singular stress concentrations that often play an important role in structure designs. The simplest engineering strength criteria are in general not appropriate due to their incapacity in dealing with important size effect induced by stress gradients. In this paper, we present first a simple experimentation, which consists of plates with a central hole under uniaxial tensile loading, showing important size effect. Second, numerous criteria, including commonly used engineering criteria, crack initiation criteria based on the finite fracture mechanics, or cohesive criteria, were adapted to fit the experimental results. We found that most of these criteria, including criteria with a single material parameter and those with two material parameters, are not suitable for fracture prediction of materials under non-singular stress concentrations. It seems that three material parameters would be the minimum to establish an adequate fracture criterion for arbitrary stress concentrations. By analysing the energy dissipation of micro-crack bands under different stress concentrations, we proposed a new fracture criterion with three material parameters based on the finite fracture mechanics. It is shown that this criterion can provide accurate critical remote loads comparing with experimental data. We believe that the three parameter concept is physically reasonable and can be used in establishing fracture criteria in both the cases of singular and non-singular stress concentrations.     

Numerical and analytical study of severity of cracks in cylindrical and spherical shells

The present study deals with the severity of cracks in pressure equipments, where such defects are often involved. Our work is particularly concerned with the problem of cylindrical shells and also the little well-known problem of spherical shells, including all sorts of practical defects, namely axisymmetric or semi-elliptic, both internal and external cracks. The stress intensity factor in the linear elastic domain and the J integral in the elastoplastic range are performed using the finite element method and compared to the results provided by the application of the semi-analytical A16 or R6 simplified criteria, depending on a limit load calculation. The nocivity of the defects depends on the crack shape and size and other structural geometrical parameters. Use is made of a polynomial decomposition of the stress field in the vicinity of the crack in order to cover all industrial loadings. All the numerical results, for a wide range of shell and crack geometries, are depicted using appropriate tables and curves in order to check the fracture criteria more easily.     

Fatigue properties and fracture analysis of a SiC fiber-reinforced titanium matrix composite

Tension–tension fatigue properties of SiC fiber reinforced Ti–6Al–4V matrix composite (SiC_f/Ti–6Al–4V) at room temperature were investigated. Fatigue tests were conducted under a load-controlled mode with a stress ratio 0.1 and a frequency 10 Hz under a maximum applied stress ranging from 600 to 1200 MPa. The relationship between the applied stress and fatigue life was determined and fracture surfaces were examined to study the fatigue damage and fracture failure mechanisms using SEM. The results show that, the fatigue life of the SiC_f/Ti–6Al–4V composite decreases substantially in proportion to the increase in maximum applied stress. Moreover, in the medium and high life range, the relationship between the maximum applied stress and cycles to failure in the semi-logarithmic system could be fitted as a linear equation: S_max/μ = 1.381 − 0.152 × lgN_f. Fractographic analysis revealed that fatigue fracture surfaces consist of a fatigued region and a fast fracture region. The fraction of the fatigued region with respect to the total fracture surface decreases with the increase of the applied maximum stresses.     

Model for prediction of simultaneous time-dependent damage evolution in multiple plies of multidirectional polymer composite laminates and its influence on creep

A model to predict time-dependent evolution of simultaneous transverse cracking developed in multiple plies during creep loading and its effects on creep of multidirectional polymer matrix composite laminates is presented. The stress states in the intact regions of the plies are determined using the lamination theory during an incremental change in time. The stored elastic energy, determined using this stress state, is compared with a critical stored elastic energy value for damage to determine if a ply would fracture after the increment. If fracture is predicted, variational analysis is used to determine the perturbation in ply stresses due to cracking. This procedure is repeated to determine the crack evolution and creep strain. Model predictions compared well with experimental results for a [±θ_m/90_n]_s laminate.     

Analytical solutions of the displacement and stress fields of the nanocomposite structure of biological materials

Biological materials, such as bone and nacre, are nanocomposites of protein and mineral with superior mechanical properties. The basic building blocks of these materials feature a generic nanocomposite structure with staggered alignment of mineral platelets in protein matrix. Because of the structural complexity of the generic structure, its displacement and stress fields are currently still unknown. In this study, a perturbation method was applied for analytically solving the displacement and stress fields of the nanocomposite structure under uniaxial tension. The effect of the elastic modulus, aspect ratio and volume fraction of mineral and protein on the displacement and stress fields in the nanocomposite structure was studied. A non-dimensional parameter γ was then suggested for characterizing the stress and strain fields in this nanostructure. We showed that the assumption of uniform shear stress distribution at the mineral-protein interface in the TSC model is valid when γ is less than 4 which is broadly applicable to most biological materials. The analytical solutions of displacement and stress fields obtained in this study provide a solid basis for further analyses of mechanical properties, such as the buckling and the fracture behaviors of biological materials.     

Measurement of resistance curves in the longitudinal failure of composites using digital image correlation

This paper presents a new methodology to measure the crack resistance curves associated with fiber-dominated failure modes in polymer–matrix composites. The crack resistance curves not only characterize the fracture toughness of the material, but are also the basis for the identification of the parameters of the softening laws used in the numerical simulation of fracture in composite materials. The proposed method is based on the identification of the crack tip location using Digital Image Correlation and the calculation of the J-integral directly from the test data using a simple expression derived for cross-ply composite laminates. It is shown that the results obtained using the proposed methodology yield crack resistance curves similar to those obtained using Finite Element based methods for compact tension carbon–epoxy specimens. However, it is also shown that, while the Digital Image Correlation based technique mitigates the problems resulting from Finite Element based data reduction schemes applied to compact compression tests, the delamination that accompanies the propagation of a kink-band renders compact compression test specimens unsuitable to measure resistance curves associated with fiber kinking.