Simple Tension Test Research Articles

Characterization of Microstructural and Mechanical Properties of 17-4 PH Stainless Steel by Cold Rolled and Machining vs. DMLS Additive Manufacturing

The 17-4 PH stainless steel is widely used in the aerospace, petrochemical, chemical, food, and general metallurgical industries. The present study was conducted to analyze the mechanical properties of two types of 17-4 PH stainless steel—commercial cold-rolled and direct metal laser sintering (DMLS) manufactured. This study employed linear and nonlinear tensile FEM simulations, combined with various materials characterization techniques such as tensile testing and nanoindentation. Moreover, microstructural analysis was performed using metallographic techniques, optical microscopy, scanning electron microscopy (SEM) with energy dispersive spectroscopy (EDS), and X-ray diffraction (XRD). The results on the microstructure for 17-4 PH DMLS stainless steel reveal the layers of melting due to the laser process characterized by complex directional columnar structures parallel to the DMLS build direction. The mechanical properties obtained from the simple tension test decreased by 17% for the elastic modulus, 7.8% for the yield strength, and 7% for the ultimate strength for 17-4 PH DMLS compared with rolled 17-4 PH stainless steel. The FEM simulation using the experimental tension test data revealed that the 17-4 PH DMLS stainless steel experienced a decrease in the yield strength of ~8% and in the ultimate strength of ~11%. A reduction of the yield strength of the material was obtained as the grain size increased.

A strain energy function for large deformations of compressible elastomers

Elastomers are typically considered incompressible or slightly compressible. However, we present simple tension and bulk tests showing that, under large deformations, these materials can undergo significant volume changes. A review of the literature reveals the lack of an accurate hyperelastic model for finite volumetric deformations of elastomers. Therefore, we propose a new volumetric strain energy density (SED) that overcomes the limitations of the current models. The main advantages of the proposed SED are: (1) accurate description of the response of rubbers for both small and large volumetric deformations; (2) ability to reproduce diverse behaviors during volume shrinkage and expansion; (3) adaptability to other compressible materials, such as soft tissues, foams and hydrogels. Using the deviatoric–volumetric split of the strain energy, the proposed volumetric SED is combined with a suitable deviatoric part selected from the literature. The parameters of the combined SED are calibrated by fitting the model to the experimental data from simple tension and bulk tests. As a result, an accurate description of the response of elastomers under both shape and volume deformations is provided. The proposed SED can be implemented in numerical codes to capture the effects of volumetric deformations on the equilibrium solutions for various stress states.

Approach for the simulation of the load-deformation behaviour of hyperelastic bonded joints using strain and strain rate dependent tangent moduli

In structural glass, Structural Sealant Glazing (SSG) systems are often used to realise facades with maximum transparency. The used silicone adhesives are currently designed in accordance to the European Technical Approval Guideline 002 (ETAG 002) by a simplified two-dimensional stress calculation concept. For a more precise calculation of the adhesive stresses and deformations, finite element analyses are used. The quality of the results, however, strongly depends on the calculation concept and material model used. In this paper, a practice-oriented viscoelastic approach using strain and strain rate dependent tangent moduli within FEA is presented. Required material parameters can be determined with a simple uniaxial tension test only. The proposed model is validated with numerous FE calculations of reality-based adhesively bonded component tests with different geometric ratios that include complex multiaxial stress states. The proposed approach allows a precise prediction of the strain state- and time-dependent stress behaviour of hyperelastic silicone bonds. The prediction quality is significantly more accurate than often used linear-elastic material models or commonly available hyperelastic models.

Modeling of hyperelasticity in polyamide 12 produced by selective laser sintering

Polyamide 12 (PA12) is a core material in many 3D-printing techniques, including selective laser sintering (SLS), and its mechanical characterization helps to better understand behaviors of additively manufactured parts made from this polymer. In this paper, the elastic response of SLS-produced PA12 is shown to be nonlinear. Standard test samples with different orientations with regard to the scanning direction are 3D-printed with the use of PA2200 powder, and their elastic response is investigated under uniaxial tension at different strain rates. Mooney–Rivlin hyperelastic models are proposed to address the observed nonlinear elasticity of the samples. Cyclic response of the specimens is shown to be stabilized after a few transient cycles so the material parameters are determined for trained samples after shakedown in their response. The obtained parameters are found to depend on the loading speed; thus, a rate-dependent hyperelastic constitutive model is presented for PA12 produced by selective laser sintering. This model is validated by comparing its numerical prediction with empirical responses under simple tension tests.

One-Dimensional Failure Modes for Bodies with Non-convex Plastic Energies

In this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109–151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109–151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution. Here, an approximate analytical solution of the evolution problem is determined in the one-dimensional case of a tensile bar. Different solutions are found describing specific plastic strain processes, and correlations between the different evolution modes and the convexity/concavity properties of the plastic energy density are established.The variety of solutions demonstrates the large versatility of the model in describing many failure mechanisms, ranging from brittle to ductile. Indeed, for a convex plastic energy, the plastic strain diffuses in the body, while, for a concave plastic energy, it localizes in regions whose amplitude depends on the internal length parameter included into the non-local energy term, and, depending on the convexity properties of the first derivative of the plastic energy, the localization band expands or contracts. Complex failure processes combining different modes can be reproduced by assuming plastic energy functionals with specific convex and concave branches.The quasi-brittle failure of geomaterials in simple tension tests was reproduced by assuming a convex-concave plastic energy, and the accuracy of the analytical predictions was checked by comparing them with the numerical results of finite element simulations.

Material Parameters Sensitivity on Springback Modelling of Simple Bending Process

Springback is one of the major defects that continuously concerns the sheet metal experts’ community. It is has long been known that the sheet thickness, the bending angle and the yield stress of the material primarily affect the angle change after the tools’ release. Besides, the consideration of the kinematic hardening (KH) model has powerful influence on the modelling results, too. In this study, we overviewed several possible factors on the springback with finite element modeling of a simple V-die bending operation, highlighting the effect of the material variables on the final shape. AutoForm® R7 software and the built-in theory of kinematic hardening were used for the material characterization, coupled with the Hockett-Sherby isotropic hardening rule as well as the Yld89 yield criterion. The material data for modeling kinematic hardening behavior were obtained by cyclic tension-compression tests, whilst the isotropic hardening and the yield surface parameters were acquired by simple uniaxial tension tests. The simulation results were compared to the experimental springback observations obtained by a CNC bending machine, without using springback compensation. A detailed parametric study was also carried out to highlight the level of criticality of the applied material variables on the final angle change.

On the determination of thermal boundary conditions for parameter identifications of thermo‐mechanically coupled material models

AbstractIdentifiability and sensitivity of thermal boundary coefficients identified alongside thermal material parameters by means of full field measurements during a simple tension test are shown empirically using a simple tension test with self heating as a proof of concept. The identification is started for 10 different initial guesses, all of which converge toward the same optimum. The solution appears to be locally unique and parameters therefore independent, but a comparison against a reference solution indicates high correlation between three model parameters and the prescribed external temperatures required to model heat exchange with either air or clamping jaws. This sensitivity is further analyzed by rerunning the identification with different prescribed external temperatures and by comparing the obtained optimal parameter values. Although the model parameters are independent, optimal values for heat conduction and the heat transfer coefficients are highly correlated as well as sensitive with respect to a change, respectively, measurement error of the external temperatures. A precise fit on the basis of a simple tension test therefore requires precise measurements and a suitable material model which is able to accurately predict dissipated energy.

Modelling of Flexible Adhesives in Simple Mechanical States with the Use of the Darijani-Naghdabadi Strain Tensors and Kirchhoff-de Saint-Venant Elastic Potential.

Practical aspects of modelling of flexible adhesives with the energy conjugate measures of stress and strain of the Darijani–Naghdabadi (D-N) family are discussed. A possibility of description of materials exhibiting non-linear physical characteristics with the use of non-linear geometric relationships and linear elastic constitutive law is considered. Nominal stress vs. stretch relations are specified in cases of simple tension and simple shear with the use of the Kirchhoff–de Saint-Venant elastic potential and D-N energy conjugate stress and strain measures. Obtained theoretical estimates were compared with experimental results of simple tension and simple shear tests performed on Sika PM polyurethane (Cracow, Sika Poland). The deformation rate was fixed in order to minimize the influence of viscosity. Values of parameters in the definition of the D-N strain tensor were optimized in order to provide good agreement between model predictions and experimental results. Observed discrepancies indicate that the proposed approach is not appropriate for constitutive modelling of the PM polymer. The presented approach is proposed to be used as a simple design model providing practical formulas describing the behavior of materials of non-linear characteristics in chosen mechanical states. Admissible values of exponents are discussed regarding its bijectivity in a limited range of variation of principal stretches.

A Novel and Highly Effective Natural Vibration Modal Analysis to Predict Nominal Strength of Open Hole Glass Fiber Reinforced Polymer Composites Structure

Glass fiber reinforced polymer (GFRP) composite laminates are considered the key material in many industries such as the infrastructure industries and the aerospace sector, and in building structures due to their superior specific strength and lightweight properties. The prediction of specimens’ nominal strength with open holes is still an attractive and questionable field of study. The specimen size effect is referred to its strength degradation due to the presence of holes when specimen geometry gets scaled. The non-destructive test used to measure the nominal strength of such material is a great tool for fast selection purposes, but not secure enough for several purposes. Furthermore, the destructive tests which are more expensive and time-consuming should be avoided in such structures. The present work aims to predict the nominal strength of open-hole GFRP’s composite using modal analysis of their natural frequency as non-destructive tests. At this end, the natural frequency, which is measured using modal analysis procedures, is combined with both linear elastic fracture mechanics (LEFM) and the theory of elasticity to predict the nominal strength of open-hole composite laminates. This advanced model employs two parameters of surface release energy resulting from a simple tension test and Young’s modulus based on vibration modal analysis. It is well established that these types of materials are also subjected to a size effect in dynamic response. Inversely to the known static loading size effect, the size effect in dynamic response increases with specimen size. The novel model gives excellent and acceptable results when compared with experimental and finite element ones. Size effects curves of a nominal strength of these laminates have a very close relative value with those obtained from finite element and analytical modeling. Moreover, the received design tables and graphs would be highly applicable when selecting suitable materials for similar industrial applications.

Identification of thermal material parameters for thermo-mechanically coupled material models

The possibility of accurately identifying thermal material parameters on the basis of a simple tension test is presented, using a parameter identification framework for thermo-mechanically coupled material models on the basis of full field displacement and temperature field measurements. Main objective is to show the impact of the material model formulation on the results of such an identification with respect to accuracy and uniqueness of the result. To do so, and as a proof of concept, the data of two different experiments is used. One experiment including cooling of the specimen, due to ambient temperature, and one without specimen cooling. The main constitutive relations of two basic material models are summarised (associated and non-associated plasticity), whereas both models are extended so as to introduce an additional material parameter for the thermodynamically consistent scaling of dissipated energy. The chosen models are subjected to two parameter identifications each, using the data of either experiment and focusing on the determination of thermal material parameters. The influence of the predicted dissipated energy of the models on the identification process is investigated showing that a specific material model formulation must be chosen carefully. The material model with associated evolution equations used within this work does neither allow a unique identification result, nor is any of the solutions for the underlying material parameters close to literature values. In contrast to that, a stable, that is locally unique, re-identification of the literature values is possible for the boundary problem at hand if the model with non-associated evolution equation is used and if cooling is included in the experimental data.

Nonlinear computation of cables with high order solid elements using an anisotropic material model

AbstractDue to their complex structure cables exhibit an anisotropic behaviour and undergo large deformations in various applications. The large deformations are simulated using blended high order solid elements that can represent large deformations efficiently. To reduce the computational complexity the cross section consisting of many single wires and different layers of material is homogenized and represented by a transversely isotropic material model. Frictional effects and possible reordering of the parts are modelled through elastoplastic material behaviour with an anisotropic yield function. The simulations show that for a simple tension test and a free torsion test the material parameters can be satisfactorily identified.

Modified nonlinear Mohr–Coulomb fracture criteria for isotropic materials and transversely isotropic UD composites

Modified nonlinear Mohr–Coulomb (M–C) fracture criteria for isotropic materials and transversely isotropic unidirectional (UD) composites are proposed in the present study. The classic linear M–C fracture criterion for isotropic materials is briefly revised, and its deficiencies and limitations are identified. Based on the modification of a nonlinear variation of the M–C criterion for UD composites, the mathematical expressions of the proposed fracture criteria are formulated. The undetermined parameters in the expressions are calibrated by the experimental data from the simple tension, compression and shear tests. The presented fracture criteria show good agreement with the test data of various kinds of isotropic materials and transversely isotropic UD composites under different stress states.

A multiplicative plastic hardening model in consideration of strain softening and strain rate: Theoretical derivation and characterization of model parameters with simple tension and creep test

Hardening behavior with its ultimate deterioration (or softening) after uniform deformation limit and strain rate sensitivity of metals at elevated temperatures are characterized. To avoid non-uniqueness in the identification procedure based on only simple tension test, an inverse identification procedure involving not only the simple tension test, but also the creep test is newly proposed. Moreover, for better understanding of creep behavior, analytical and numerical creep models are developed for the generalized multiplicative constitutive law accounting for hardening, softening, and strain rate sensitivity. Robust parametric studies are presented to explore the effect of material and process parameters on creep deformation behavior, which is also effectively used for the two-step characterization procedure of the proposed hardening model. The identification procedure for the multiplicative constitutive model is demonstrated using AZ61 Mg alloy sheet, which provides good correlations between calculated and measured stress-strain curves and creep strains under different strain rates and prior-creep strains.

Numerical investigation on the influence of the electro-resistance welding pipe manufacturing process on the local variation of the yield strength of the pipe material

In the present research work, a finite element model of the electro-resistance welding pipe forming process chain is developed using the ABAQUS/Explicit software. The forming process, which is composed of 22 tandem roll stations, has been fully modeled in the developed finite element simulation. In order to account for the Bauschinger effect on the pipe material properties as a consequence of the loading and the unloading during the process, a non-linear kinematic hardening model has been utilized in all the proposed finite element simulation models. The constants for the non-linear kinematic hardening model were estimated by means of cyclic experiments on the K55 steel pipe material. In order to properly simulate the electric arc welding (electro-resistance welding) operation, the ABAQUS welding interface has been utilized to account for the joining between the two edges of the formed pipe as well as to assess the influence of the welding-induced temperature field on the residual stresses on the pipe material. The sizing operation, which is the final station of the electro-resistance welding process, has been also accounted in the developed finite element method model and is composed of six tandem rolls. To export and import the results between two different modules, a mapping strategy has been utilized and allowed exporting the element results, in terms of stress, strain, and temperature, and importing them into the following simulation module. Finally, in order to estimate the influence of each process station on the yield strength of the material, a finite element simple tension test simulation has been implemented in ABAQUS/Static, mapping the results of each station on the tensile specimen. This mapping operation allowed to estimate the yield stress of the material after each of the three process stations, a consequence of the residual stresses present in the material, and has been carried out on eight circumferential locations around the pipe, evenly spaced with a 22.5° angle. The model has been validated by comparing the geometrical results, in terms of average pipe diameter and thickness, obtained from the finite element model with those of the relevant industrial production, showing deviations equal to 1.25% and 1.35% (forming) and 1.29% and 1.43% (sizing), respectively, proving the reliability of the proposed process chain analysis simulation. The results will show how the process-induced residual stresses arising on the pipe material make the material yield strength to vary from station to station as well as having different values along the circumferential direction of the pipe.

A deformation detection method for aircraft skin on uniform pressure by using speckle image correlation technology

The fatigue cracks of aircraft skin which are caused by the pressurization for a civilian airplane during the flight process will bring potential serious safety risks. Therefore, it is necessary to study the deformation mechanism for the aircraft skin on uniform pressure. Traditional fatigue testing machines can only be used for simple tension and compression tests which cannot be applied directly. This paper proposes a deformation detection method by using speckle image correlation technology. Firstly, a fatigue testing machine simulating uniform pressure has been designed. Secondly, a speckle image correlation method by using improved KLT (Kanade-Lucas-Tomasi) algorithm is presented to obtain the coordinates of the coated speckle spots. Finally, static and dynamic experiments were implemented to verify the accuracy and effectiveness of the proposed method. In conclusion, this method can be applied in airworthiness certification to improve the testing efficiency.

Inferring Post-Necking Strain Hardening Behavior of Sheets by a Combination of Continuous Bending Under Tension Testing and Finite Element Modeling

This paper presents a combined experimental and simulation approach to identify post-necking hardening behavior of ductile sheet metal. The method is based on matching a measured load-displacement curve from a continuous bending under tension (CBT) test with the curve simulated using the finite element method (FEM), while adjusting an input flow stress curve into the FEM. The CBT test depletes ductility uniformly throughout the gauge section of a tested sheet, and thus, stretches the sheet far beyond the point of maximum uniform strain in a simple tension (ST) test. Having the extended load-displacement curve, the calibrated flow stress curve is extrapolated beyond the point of necking. The method is used to identify the post-necking hardening behavior of an aluminum alloy, AA6022-T4, and two dual-phase (DP) steels, DP 980 and DP 1180. One measured load-displacement curve is used for the identification of a flow stress curve per material, and then the flow stress curve is used to simulate two additional measured load-displacement curves per material for verification. The predictions demonstrate the utility of the developed CBT-FEM methodology for inferring the post-necking strain hardening behavior of sheets. Furthermore, the results for AA6022-T4 are compared with the hydraulic bulge test data. Unlike the hydraulic bulge test, the CBT-FEM method can predict increasing as well as decreasing anisotropic hardening rate in the post-necking regime. The latter is associated with probing stage IV hardening. The proposed methodology along with the results and these key advantages are presented and discussed in this paper.

Strength and fracture behaviour of polymer matrix composite layered structures made by additive manufacturing

In this paper, studies on the tensile strength, fracture initiation and propagation behaviour of composite material layered shell structures manufactured by extrusion based additive manufacturing (AM) is reported. To understand the basic mechanical behaviour, simple tension tests have been conducted on ASTM-D638 specimens of carbon fiber and natural fiber reinforced polymer matrix composites made by AM in different modes as well as directly in filament form using a filament extruder. The tensile strengths reveal that the internal defects unique to additive manufacturing, such as lack of fusion (LOF) sites and voids, play crucial role in the macroscopic fracture. Based on the tensile test results, finite element analysis of shell structures typical of below-knee prosthetic sockets has been conducted to predict the fracture initiation sites and propagation paths. The analysis results have shown close correlation with the experimental observation of the fracture phenomenon in the prosthetic sockets given to pilot test amputees.

Effect of fiber volume fraction on the mechanical properties of randomly oriented glass fiber reinforced polyurethane elastomer with crosshead speeds

The effect of fiber length and fiber volume fraction at different crosshead speeds on the mechanical properties and toughness of randomly oriented glass fibers reinforced polyurethane elastomer composites were studied using standard simple tension test. The modulus of elasticity and the yield stress increase with increasing the fiber volume fraction, the fiber length and the crosshead speed. The percentage increase due to the increasing of fiber volume fraction for 10 mm fiber length is much higher than that for 5 mm fiber length, while the percentage increase due to increasing of the crosshead speed for 10 mm fiber length is lower than that for 5 mm. The toughness of the failed specimens decreases with increasing the fiber volume fraction, the crosshead speed and fiber length.

Fatigue analysis of shape memory alloy helical springs

Estimating the functional as well as structural fatigue life of shape memory alloy (SMA) components has become a challenging issue for researchers. In current work, by considering the effects of large deformations, a rate-dependent energy-based model is developed to predict behavior of SMA helical springs under cyclic mechanical loadings. The effects of strain rate, convective heat transfer coefficient, and mean applied displacement to an SMA spring on its responses are investigated. SMA springs are fabricated through shape setting NiTi wires, and simple tension and fatigue tests are conducted on the fabricated specimens at different temperatures. Fatigue curves are presented in terms of variations in the amount of dissipated energy in stabilized force-displacement response with the number of cycles to failure. The amount of dissipated energy is calculated using the developed model, and the theoretically-predicted fatigue lives are shown to be in a good agreement with experimental results. Therefore, the presented approach is found to be a reliable method to predict lifetime of SMA springs in practice. The fatigue curves confirm the influence of loading frequency on the fatigue life.

Application of Digital Image Correlation (DIC) to the Measurement of Strain Concentration of a PVA Dual-Crosslink Hydrogel Under Large Deformation

Hydrogels are a class of soft, highly deformable materials formed by swelling a network of polymer chains in water. With mechanical properties that mimic biological materials, hydrogels are often proposed for load bearing biomedical or other applications in which their deformation and failure properties will be important. To study the failure of such materials a means for the measurement of deformation fields beyond simple uniaxial tension tests is required. As a non-contact, full-field deformation measurement method, Digital Image Correlation (DIC) is a good candidate for such studies. The application of DIC to hydrogels is studied here with the goal of establishing the accuracy of DIC when applied to hydrogels in the presence of large strains and large strain gradients. Experimental details such as how to form a durable speckle pattern on a material that is 90% water are discussed. DIC is used to measure the strain field in tension loaded samples containing a central hole, a circular edge notch and a sharp crack. Using a nonlinear, large deformation constitutive model, these experiments are modeled using the finite element method (FEM). Excellent agreement between FEM and DIC results for all three geometries shows that the DIC measurements are accurate up to strains of over 10, even in the presence of very high strain gradients near a crack tip. The method is then applied to verify a theoretical prediction that the deformation field in a cracked sample under relaxation loading, i.e. constant applied boundary displacement, is stationary in time even as the stress relaxes by a factor of three.