Tearing energy of AZ31 magnesium alloy sheets determined by the multiple tensile testing method

Tearing energy of the AZ31 magnesium alloy sheets in the annealed (O-tempered) and half-hard (H24) conditions was studied in both rolling and transverse directions by the multiple tensile testing method. The results showed that while plastic deformation energy was primarily controlled by the strain hardening exponent, tearing energy was directly related to the neck breadth parameter N, which depends on the strain hardening, strain rate hardening, and plastic anisotropy of the tested sheets. It was also found that the tearing energies obtained for the annealed AZ31 sheets were comparable to those of AA5010 aluminium sheets, while the plastic deformation energies were much higher than those of aluminium sheets. This may imply that AZ31 magnesium sheets can be potential candidates for dissipating the impact energy in the vehicles structures which are prone to collision.     

Deformation energy of NiTi shape memory wires

Deformation energy of NiTi wires with B2 and R phases was studied by the multiple tensile testing (MTT) method. In traditional materials, the total energy required to tear specimens is assumed to be the sum of elastic, uniform plastic, and post-uniform or tearing energy components. For the shape memory alloys, however, this classification is not valid due to their unusual superelastic/shape memory characteristics. Using a modified MTT method, different energy components were calculated by plotting different combination of deformation energies divided by the specimen cross-sectional area against the gage length of the specimens. The slope of the obtained straight line demonstrates the summation of the elastic, superelastic/shape memory, second elastic, and plastic energy per unit volume and its intercept gives the value of tearing energy. It was found that the uniform plastic energy per unit volume for the R-phase wires was considerably higher than that for the B2-phase wires. This caused a marked enhancement in the total deformation energy of the R-phase wire, as compared to the B2-phase wire. The effect of strain rate on the tensile behaviour and deformation energies of these materials was also investigated. Except the plateau stress of the tensile curve which was raised for both wires, the B2-phase wires were almost strain-rate-independent, whereas the R-phase wires were significantly influenced by the variation in strain rate.     

Buckling and fracture behaviour of cracked thin plates under shear loading

Thin-walled structural components are widely used in several engineering applications such as in aerospace, naval, nuclear power plant, pressure vessel, mechanical and civil fields. Since they are frequently characterised by a high slenderness, the safety assessment of such structural components requires to carefully consider the buckling collapse which can heavily limit their allowable bearing capacity. For very thin plates, buckling collapse can occur under compression, shear, or even under tension. In the present paper, the buckling and fracture collapse mechanisms in an elastic rectangular thin-plate with a central straight crack under shear loading are analysed. Different boundary conditions, crack length and orientation are considered. Through a parametric finite elements (FE) numerical analysis, the crack sensitivity of the collapse load of such a structural component is examined. The obtained results are discussed, and some interesting and useful conclusions are drawn. The collapse mechanism occurring earlier (buckling or fracture) is found by varying the fracture toughness of the material, and some failure-type maps depending on the geometrical parameters of the crack are determined.     

J integral solution for semi-elliptical surface crack in high density poly-ethylene pipe under bending

The goal of this work is to analyse the severity of semi-elliptical crack defects and to study the degree of damage in the poly-ethylene pipe in bending during the crack propagation. The semi-elliptical cracks are considered in this work located in different position in the wall of the pipe. The three finite element method based on the computation of the J integral was used to analyse the fracture behaviour of these structures. The effect of the position, shape and size of the crack on the J integral values was highlighted. The effects of strain rate and the temperature on the J integral values were also examined. The obtained results show that the strain rates have a strong influence on the J integral values especially for circumferential crack at higher bending moment. However, the energy for circumferential crack is more important compared to axial crack. The effect of the depth of the crack becomes important when the ratio (a/t) reaches a critical value of 0.6 (a/t = 0.6), especially when the ratio a/c is weak (semi-elliptical crack, a/c = 0.2) where the J integral values becomes independently of the crack depth, this conclusion is opposite to the above for the poly-ethylene pipe subjected to internal pressure. We recall finally, that the temperature effect on circumferential cracks behaviour is more important compared to the axial cracks at critical crack size (a/c = 0.2 and a/t = 0.6). It is also shown that in the wall of pipe, the internal cracks are more dangerous than the external cracks.     

Some applications of Burzyński yield condition in metal plasticity

The classical J₂ plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure-sensitive yielding or plastic dilatancy. Another difficulty is the difference between the values of yield stresses in tension and compression for isotropic materials, the so-called strength differential effect (SD), leading to the asymmetry of the elastic range. The Burzyński yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto-plastic constitutive equations for the paraboloid case of Burzyński’s yield condition is formulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial Finite Element code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plasticity theory with the paraboloid case of Burzyński’s yield condition describes adequately the strength differential effect, which is present in many kinds of materials significant for recent applications.     

Joining phenomena and tensile strength of friction welded joint between pure titanium and low carbon steel

This paper describes the effect of the friction welding condition on the joining phenomena and the tensile strength of friction welded joint between pure titanium (P-Ti) and low carbon steel (LCS). The adjacent region of the weld interface at the P-Ti side was intensely upsetting with accompanied large deformation of itself when the joint had sparkle at both applied friction pressures of 30 and 90 MPa, although that of the LCS side was hardly upset. The temperature of the whole weld interface at a friction pressure of 30 MPa reached to 1150 K or over at a friction time of 3.0 s or longer. However, the half radius and centreline portion temperatures of the weld interface at a friction pressure of 90 MPa was not reached to 1150 K, although the periphery portion of that was reached to its temperature. The central portion of the weld interface at a friction pressure of 90 MPa was deformed to a convex shape from the viewpoint of the P-Ti side, although that of 30 MPa remained almost flat after when the friction torque reached the initial peak. When the joint was made at a friction pressure of 30 MPa, a friction time of 3.0 s or longer, and a forge pressure of 270 MPa or higher, it achieved 100% joint efficiency and the P-Ti base metal fracture with no crack at the weld interface. However, many joints at friction times of 1.2 and 1.5 s fractured at the weld interface, although those achieved 100% joint efficiency, because whole weld interface temperature was below 1150 K. On the other hand, many joints at a friction pressure of 90 MPa with high forge pressure also fractured at the weld interface, although those achieved 100% joint efficiency, because the weld interface temperature at the half radius and periphery portions was below 1150 K. Those joints did not have the intermetallic compound layer at the weld interface. The difference of the fractured portion of the joint in both applied friction pressures was due to the difference between the maximum temperature at the weld interface during the friction process and the deformation amount of the LCS side caused by applied forge pressure. To obtain 100% joint efficiency with the P-Ti base metal fracture with no crack at the weld interface, the joint should be made with high forge pressure, low friction pressure, and with opportune friction time at which the temperature at whole weld interface reached around 1150 K.     

Split Hopkinson pressure bar testing of 3D woven composites

Results from a series of split Hopkinson pressure bar (SHPB) tests on 3D woven tetxile composites (3DWC) are presented. These tests were done to determine the rate dependent compression response of 3DWC. Three different configurations of the 3DWC, corresponding to compression response in the plane of the material and through-the-thickness direction (out-of-plane) were studied. The rate dependent responses were compared against quasi-static test results and it was found that 3DWC showed an increase in strength in all three directions studied, however, accompanied by a transition in the failure mechanism. The in-plane orientations showed the largest increase in (about 100%) strength at the elevated rates of loading. A follow-on paper provides finite element based results that correspond to the experimental results presented here.     

Optimisation of process parameters in flanging operation in order to minimise stresses and Lemaitre’s damage

The objective of this work is modelling and optimisation of sheet bending process by means of numerical simulation. One of the problems to be solved in the sheet metal forming processes of thin sheets is the taking into account of the effects of technological process parameters so that the part takes the desired mechanical characteristics. Accordingly, it has been a crucial research subject for designing bending tools guaranteeing an optimal performance of products in terms of mechanical properties and good rigidity. In this paper, we propose a numerical procedure allowing the definition of the optimal values of process parameters in flanging operation, which minimises the residual stresses and the material damage at the end of the bending phase. The concept of continuum damage mechanics fully coupled with elasto-plasticity has been retained to describe the progressive damage accumulation into the sheet metal. According to parametric investigation on the maximum stress and calculated damage values, it has been found that the punch-die clearance and the die radius have significant effects on mechanical behaviour of parts. An application of design of experiments was developed as a preliminary step for the optimisation of the process parameters by using response surface methodology. This model allows the identification of the influential parameters of an optimisation problem and the reduction of the number of evaluations of the objective function.     

Effect of brazing temperature on tensile strength and microstructure for a stainless steel plate-fin structure

This paper presented a vacuum brazing technology for 304 stainless steel plate-fin structures with BNi2 filler metal. The effect of brazing temperature on tensile strength and microstructure has been investigated. The tensile strength is increased along with the increasing of brazing temperature. The microstructure is very complex and some Boride compounds are generated in the brazed joint. Full solid solution can be generated in the middle zone of joint when the brazing temperature is increased to 1100 °C. The brittle phases always exist in the fillet no matter how the brazing temperature changes, but the microstructure in fillet becomes more uniform and the tensile strength is increased with the brazing temperature increasing. In total, the brittle Boride compounds are decreased with the brazing temperature increase. Brazing with a filler metal thickness 105 μm and 25 min holding time, 1100 °C is the best suitable brazing temperature and a tensile strength of 82.1 MPa has been achieved for 304 stainless steel plate-fin structure.     

Fracture in bending – The straining limits of monolithic sheets and machined tailor-made blanks

This paper studies fracture in the bending of monolithic sheets and machined tailor-made blanks made of high strength aluminum alloys commonly used in the aircraft industry as well as the effects of sheet thickness and thickness difference on their forming limits. Tailor-Made Blanks (TMBs) are sheet metal assemblies that are composed of sheets with different thicknesses and/or materials. Machining is among the techniques that can be used for creation of the needed thickness variations and is the one that is studied in this paper, because it isolates the effects of thickness difference from those of the welding/joining process. The selected materials are 2024-T3 and 7075-T6 representing 2000 and 7000 series aluminum alloys. Two sets of experiments are carried out to identify the effects of sheet thickness and thickness difference on the forming behavior of the selected alloys. The first set of the experiments is tensile testing. The tensile properties of sheets with different thickness and thickness ratios including the plasticity parameters are determined in the first set of experiments. The second set of the experiments is air bending. The minimum bending radii of materials with different thicknesses and thickness ratios are determined in the second set of experiments. Then, the forming limits are determined using a theoretical approach and the experimentally-determined forming limits are compared with the theoretically-determined ones. The results of the tensile testing and air bending are studied both separately and in comparison with each other to identify the trends and to understand the mechanisms governing the observed trends. It is shown that the minimum bending ratio increases as the sheet thickness increases and that the minimum bending radius slightly (10–12%) increases as the thickness ratio increases from 1 to 2.     

Pseudo-elastic description of polymeric foams at finite deformation with stress softening and residual strain effects

Polymeric foams are typical materials for energy absorber in such areas as aircraft, car industry and in the field of electronic packaging. Besides the typical hyperelastic behaviour, non-linear stress–strain behaviour in large elastic deformation, polymeric foams may also exhibit some inelastic effects, like stress softening and residual strain. In this paper we first describe some experiment results that illustrate the stress softening in compressible expanded polypropylene (EPP) foams together with associated residual strain effects. Then, based on Ogden and Dorfmann’s results, a pseudo-elastic model is introduced to capture the stress softening and residual strain effects by including of two variables in the energy function. Numerical simulations of uniaxial-compression tests of two types of EPP foam are used to determine the material parameters of Ogden’s model, stress softening and residual strain effects. The numerical simulations indicate that the pseudo-elastic model provides reasonably accurate predictions of the inelastic behaviour of polymeric foam.     

Predictive equations of the tensile properties based on alloy hardness and microstructure for an A356 gravity die cast cylinder head

One of the main problems in the design of complex Al–Si cast components is the wide variety of mechanical properties in different regions of the castings which is due to the wide range of solidification microstructures, related to the local solidification conditions. There are many papers available on the widely used A356/A357 Al–Si–Mg alloys, however, most experimental data on their tensile or fatigue properties are generally obtained from specimens cast separately or produced under controlled laboratory conditions, that are extremely different from those of industrially cast components. Moreover, most of these data often relate the mechanical properties to only one microstructural parameter, such as solidification defects or secondary dendrite arm spacing, and do not take their simultaneous effect into consideration. For all these reasons, the main problem, in the design phase, is the lack of knowledge of the true local mechanical properties in complex-shaped castings, which often means a conservative approach is necessary, with a consequent increase in thickness and therefore in weight. The aim of this research was to study a complex A356 gravity die cast cylinder head, in order to verify the range of variability of the main microstructural parameters and tensile properties, using specimens directly machined from the casting. The component was heat treated at the T6 condition, and the effect of the delay between quenching and aging on the alloy hardness was also evaluated. Simple experimental equations have been proposed, able to successfully predict the local tensile properties in the casting, when only the most important microstructural parameters and alloy hardness are known. These equations allow the designer to predict the local tensile behaviour without any tensile tests; moreover they can also link the post-processing results of the casting simulation software to the pre-processing phase of the structural ones, with an approach of co-engineered design.     

Numerical analysis of panels’ dent resistance considering the Bauschinger effect

The Bauschinger effect should be considered in the analysis of panels’ dent resistance, because sheet metal experiences a complex loading history from stamping to denting. This paper studies the modeling and simulation of panels’ static dent resistance, taking the Bauschinger effect into consideration. Our work covers two parts: simulation and experiment. Procedures of drawing, springback I, indenting and springback II are simulated in a multiple step analysis. Different hardening models, including the isotropic hardening model, the linear kinematic hardening model and the nonlinear combined hardening model are used, respectively, in simulation. Comparing the simulation results with the experiment results, we find that the Bauschinger effect has a great influence on panels’ dent resistance. When panels are made of high strength steel or stamped with a high Blank Holder Force (BHF), the Bauschinger effect on panels’ dent resistance is more severe. Considering the effect in numerical analysis would improve the simulation accuracy effectively. The work of this paper is beneficial to material selection and processing optimization for automobile exterior panels.     

Two-step method to evaluate equibiaxial residual stress of metal surface based on micro-indentation tests

The present study proposed a method to evaluate the equibiaxial compressive residual stress of a metal surface by means of a depth-sensing indentation method using a spherical indenter. Inverse analysis using the elastic–plastic finite-element model for an indentation test was established to evaluate residual stress from the indentation load–depth curve. The proposed inverse analysis utilizes two indentation test results for a reference specimen whose residual stress is already known and for a target specimen whose residual stress is unknown, in order to exclude the effect of other unknown mechanical properties, such as Young’s modulus and yield stress. Residual stress estimated by using the indentation method is almost identical to that measured by X-ray diffraction for indentation loads of 0.49–0.98 N. Therefore, it can be concluded that the proposed method can effectively evaluate residual stress on metal surface.     

Effects of exposure to elevated temperatures and subsequent immersion in water or alkaline solution on the mechanical properties of pultruded BFRP plates

In this article, a pultruded unidirectional basalt fiber-reinforced polymer (BFRP) plate was thermally aged at 135 °C and 300 °C for 4 h, and subsequently immersed in distilled water or strong alkaline solution (simulating concrete pore water, pH = 12.6–13) for 3 months. The variation of the tensile and interlaminar shear (ILSS) properties of the BFRP plates was studied. Thermal aging exhibited a slight effect on both the longitudinal tensile properties and the interlaminar shear strength, although thermal decomposition of the resin matrix started at 300 °C and brought in a high void content (4.8%). FTIR and DMTA results indicate that thermal aging lead to postcuring and oxidation of the resin matrix, leading to an increase of the glass transition temperatures. Thermal aging accelerated the degradation of the BFRP plates in distilled water or alkaline solution at 20, 40 and 60 °C. In the studied hash immersion conditions of 60 °C alkaline solution for 3 months, the unaged, 135 °C aged and 300 °C aged BFRP samples showed reduction in the tensile strength by 43.2%, 62.3% and 74.1%, respectively. The higher the thermal aging and immersion temperatures, the more deterioration of the mechanical properties occurred. Alkaline solution immersion showed more adverse effects compared to the distilled water. The detrimental effects of the thermal aging were attributed to the formation of voids and cracks through which water or alkaline solution tended to easily penetrate into the BFRPs. The degradation of the resin due to thermal aging and immersion was analyzed with dynamic mechanical thermal analysis and scanning electron microscopy analysis. The long term variation of the tensile strength of BFRPs was evaluated based on the Arrhenius equation.     

A critical comparison of various data processing methods in simple uni-axial compression testing

The paper compares the error associated with various data processing methods to obtain true stress–plastic strain data from the load–deformation curves generated from uni-axial compression tests. Towards this end, uni-axial compression tests have been conducted on three representative materials viz. modified 9Cr–1Mo ferritic steels, alloy D9 (a titanium modified austenitic stainless steel) and 316L(N) austenitic stainless steel in wide ranges of temperatures and strain rates. It has been observed that the absolute average error associated with maximum true plastic strain calculation in all the three materials is always more than 5% and sometimes as high as 42.1% if the elastic region is removed either from the load–stroke curve or engineering stress–strain curve to get the true stress–plastic strain curve. However, the absolute average error associated with plastic strain calculation is always less than 5% if the elastic region is removed from the true stress–strain curve.     

Low velocity localized impact study of cellular foams

This paper deals with low velocity impact behavior of two densities of ductile polyvinylchloride (PVC) foam manufactured by Divinicell. Low velocity impact tests are carried out on foam beam and panel specimens. A drop-weight rig is used to carry-out the impact tests. The test rig is equipped with a load cell connected to a data acquisition PC computer, which allows the most important dynamic and kinetic parameters, such as the contact force, load–time response, impactor velocity and energy to be measured. Post-impact creep response of the foam is also investigated. Finite element analyzes are also conducted to study the dynamic response of foam specimens subjected to a low velocity impact. The present paper contributes towards the development of a damage tolerance design approach for structural foams.     

Effects of environmental ageing on the static and cyclic bending properties of braided carbon fibre/PEEK bone plates

The use of titanium and steel bone plates to fix fractured limbs can create problems due to stress shielding, bone resorption and subsequent refracture. Here, braided carbon fibre reinforced poly-ether-ether-ketone (CF/PEEK) was evaluated as a possible implant material that could reduce these problems. CF/PEEK bone plates were aged in a simulated body environment for up to 12 weeks and then mechanically tested in 3 and 4-point bending tests. Sample mass increased by around 0.3 wt.%, yet bending stiffness and strength remained unchanged. Scanning Electron Microscopy (SEM) showed no changes in failure modes with age. Braided CF/PEEK shows an excellent resistance to fatigue failure even after prolonged ageing, easily surpassing the fatigue life of commonly used stainless steel alloys such as 316L. In addition, CF/PEEK had half the stiffness of steel for the same static strength, which would reduce stress shielding. Together, the results suggest that CF/PEEK is a highly suitable material for bone plates and should be further investigated for this application.     

Three dimensional elasticity solution for static and dynamic analysis of multi-directional functionally graded thick sector plates with general boundary conditions

In this study, the three dimensional static and dynamic behavior of a thick sector plate made of two-directional functionally graded materials (2D-FGMs) is investigated. Material properties are assumed to be graded in both radial and thickness directions according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the 3D theory of elasticity. Employing 3D graded finite element method (GFEM) based on the Hamilton’s principle and Rayleigh–Ritz energy method, the equations are solved in space and time domains. In the case of static analysis, the sector plate is subjected to a uniform pressure load and for dynamic analysis is subjected to an impact loading. The effects of material gradient index, boundary condition and thickness to radius ratio of the sector plate on the static and dynamic responses are presented and discussed.     

Comparative investigations on numerical modeling for warm hydroforming of AA5754-O aluminum sheet alloy

This study aimed to determine the proper combinations of numerical modeling conditions (e.g. solver, element type, material model) for warm hydroforming of AA5754-O aluminum alloy sheets. Assessment of finite element analyses (FEA) is based on comparison of numerical results and experimental measurements obtained from closed-die forming, hydraulic bulge and tensile tests at different temperature (25–300 °C) and strain rate (0.0013–0.013 1/sec) levels. Thinning (% t) and cavity filling ratios (CFR) on the formed parts were taken as comparison parameters. Several numerical analyses employing different element types, solution methods and material models were performed using the commercially available FEA package LS-Dyna to determine the best combination of modeling options to simulate the actual warm hydroforming operation as accurately as possible. Analyses showed that relatively better predictions were obtained using isotropic material model, shell elements and implicit solution technique when compared with experimental results.