True Strain Values Research Articles

Memory effect of spider major ampullate gland silk in loading-unloading cycles and the structural connotations

Spider silk is repeatedly stretched while performing biological functions. There is a close relationship between the shape change of the fibre materials and their mechanical properties. However, the effect of the deformation and interval time on the structure and tensile behaviour properties of spider silk after repeatedly stretching by given strain value has been rarely reported. Here we found that spider major ampullate gland silk (MAS) can revert its tensile behaviour independent of its previous loading history via intervals of approximately 8 s to 5 min with constant and increased elongation, respectively, after being subjected to yield and hardening regions. The true stress-true strain curve beyond a given value of true strain is independent from the previous loading history of the sample. Even after longer intervals (≥1 h), MAS can reproduce the last tensile behaviour via one stretched. Despite recognizing the development of irreversible deformations in the material when tested in air, the reversible change in tensile behaviour outside the spider silk's elastic region has rarely been observed before. MAS has at least one proper ground state that allows it to present good shape and mechanical behaviour memory in terms of longitudinal stretching, functioning as a new strategy to achieve certain tensile properties. The analysis of the true stress–true strain curves was performed from a series of loading‒unloading tests to evaluate the evolution of those mechanical parameters with the cycle number. The elastic modulus measured in the loading steps increases monotonously with increasing values of true strain reached in the cycles. In contrast, a marginal variation is found in the values of the yield stress measured in the different cycles. The memory and variation in the mechanical behaviour and performance of MAS can be accounted for through the irreversible and reversible deformation micromechanisms and its combination in which the viscoelasticity of the material plays a leading role. These findings may be helpful to guide the biomimetic design of novel fibre materials such as spider silk gut via artificially stretching spider silk glands.

Effect of Severe Torsion Deformation on Structure and Properties of Titanium–Nickel Shape Memory Alloy

In the present work, the possibility of applying severe torsion deformation (STD) to a bulk near-equiatomic NiTi shape memory alloy in order to accumulate super-high strain and improve mechanical and functional properties was studied. STD was performed using the multidirectional test system “BÄHR MDS-830” at a temperature of 500 °C (the upper border temperature for the development of dynamic polygonization) in 14 and 30 turns with accumulated true strain values of 4.3 and 9.1, respectively. Structural phase state and properties were studied using differential scanning calorimetry, X-ray diffractometry, transmission electron microscopy, hardness measurements, and thermomechanical bending tests. STD at 500 °C allowed for the accumulation of high strain without failure. As a result of STD in 30 turns, a submicrocrystalline structure with an average grain/subgrain size of about 500 nm was formed. This structure ensured the achievement of high maximum completely recoverable strain values of 6.1–6.8%. The results obtained show the prospects of applying severe torsion straining deformation to titanium nickelide in terms of forming an ultrafine-grained structure and high properties.

Evaluation of hole expansion ratio of ultra-high strength martensitic steels produced with various processing routes

Hole expansion ratio of hot rolled ultra-high strength martensitic steels with tensile strength around 1000 MPa was evaluated. Steels were produced with direct quenching and traditional reheat and quenching processes with final thickness of 3 mm. Achieved yield strength values (Rp0.2) varied between 918 – 1068 MPa depending on the processing route. Mean hole expansion ratios (HER) in direct-quenched (DQ) and direct-quenched and tempered (DQT) conditions were between 22 – 36 %, and no clear improvement was seen after tempering treatment compared to quenched variant. HER values for reheat and quenched (RQ) and reheat, quenched and tempered (RQT) variants were between 31 – 49 %, and the highest values were achieved with RQT steels, which were tempered at 600 °C. Based on the field emission scanning electron microscope with electron backscatter scanning diffraction (FESEM-EBSD) analysis/characterization of martensite grain size, more uniform grain structure was discovered in RQ steels, which could be the reason for improved HER properties. HER values were also compared to tensile test results (uniform elongation, true thickness strain), and formability maps were constructed. However, only minor correlation was found between HER and true thickness strain values.

Mechanical anisotropy and fracture behaviour of bulk ultra-fine grained AA2099 alloy

ABSTRACT In this work, the effect of cryo-deformation and post-deformation annealing process on tensile, anisotropic and fracture behaviour of AA2099 has been investigated. The development of ultrafine-grained (UFG) microstructure is achieved initially by cryorolling (CR) process on the solution-treated (ST) alloy by subjecting it to a true strain value of 2.3. Cryorolled samples are then followed by annealing process at temperatures of 150°C (CR + 150°C) and 200°C (CR + 200°C). A notable improvement in yield strength (~342 MPa), ultimate tensile strength (~472 MPa), hardness (~138 HV) and fracture toughness parameters (K Q (31.8 MPa √ m ), K ee (31 MPa √ m ) and J integral (57.67 kJ/m2)) is recorded, whereas anisotropy increases in the rolling direction and ductility show a significant drop at CR sample condition in comparison with coarse grains at ST condition. When annealing was executed at 150°C and 200°C, notable improvements in tensile, anisotropic and fracture behaviour of UFG AA2099 were observed. There has been a significant enhancement in tensile strength, anisotropy and fracture toughness until temperature reaches 150°C being the highest (~506 MPa), whereas after 150°C, these properties have been shown to decrease notably.

Analysis of the limiting states of cylindrical elastic-plastic shells under tension and combined loading by internal pressure and tension

The elastic-plastic deformation, limiting states and supercritical behavior of cylindrical shells under tension and combined loading by internal pressure and tension to failure are studied theoretically and experimentally. This problem is characterized by the occurrence of large strains, shape changes and, as a result, an inhomogeneous stress-strain state. In the numerical solution of such problems, the problem arises of constructing true stress-strain curves of materials. In this regard, to study the deformation and strength properties of materials, it is important to use an experimental-computational approach, which makes it possible to take into account the non-uniaxiality and inhomogeneous of the stress-strain state without accepting simplifying hypotheses. The paper presents a new efficient algorithm for constructing a true stress-strain curve, which is based on the procedure of nonlinear extrapolation of the curve. Such an algorithm, in the process of direct numerical solution of the problem, consistently constructs a stress-strain curve without using repeated direct calculations, which significantly (at times) increases its efficiency. Based on the experimental-computational approach, the true stress-strain curves for solid rods and shells made of 10KhSND and 10G2FBYu steels were determined under tension and combined loading by internal pressure and tension to failure. The failure of shells under tension occurs at lower (at times) values of true strain than solid rods. Significant differences in true stresses and strains at the moment of failure are due to different localization of deformation of solid rods and shells after the loss of stability of plastic deformation in tension. It is shown numerically and experimentally that after loss of stability of plastic deformation according to Considerer in tension, the cylindrical shell contains two forms of loss of stability until the moment of failure. The first form of loss of stability, as in solid rods, is characterized by localization of deformations along the diameter of the sample in the form of a neck, and the second form is characterized by localization of deformations along the thickness of the sample, which determines the final stage of failure. Under the action of internal pressure on the shell, the first form of loss of stability of plastic deformation degenerates with the formation of a neck inside the shell, and only the form of loss of stability is observed, caused by the localization of deformations along the thickness of the shell.

Mechanical Properties and Structure of High-Purity Niobium Sheets for the Superconducting RF Cavities

Accelerators are used in many areas of modern science and technology (FCC-ee, CEPC, ILC, ESS, MYRRHA, etc.). One of the main elements of accelerators is the superconducting cavity based on high-purity niobium sheets. In addition to RRR requirements (over 300) niobium sheets for the SRF cavities should meet rather tough requirements for the grain size, recrystallization degree and mechanical properties. Development of the manufacture regimes of the niobium sheets with the required characteristics for the SRF cavities is a promising and relevant task. The paper presents the study results of the deformation route, true strain value, recrystallization heat treatment regimes influence on the structural and mechanical characteristics of the high-purity niobium sheets.

Coarse‐Grained Refractory Composite Castables Based on Alumina and Niobium

Niobium‐alumina composite aggregates with 60 vol% metal content and with particle sizes up to 3150 μm are produced using castable technology followed by sintering, and a crushing and sieving process. X‐Ray diffraction (XRD) analysis reveals phase separation during crushing as the niobium:corundum volume ratios is between 37:57 and 64:31 among the 4 produced aggregate classes 0–45, 45–500, 500–1000, and 1000–3150 μm. The synthesized aggregates are used to produce coarse‐grained refractory composites in a second casting and sintering step. The fine‐ and coarse‐grained material shows porosities between 32% and 36% with a determined cold modulus of rupture of 20 and 12 MPa, and E‐moduli of 37 and 46 GPa, respectively. The synthesized fine‐grained composites reached true strain values between 0.08 at 1100 °C and 0.18 at 1500 °C and the coarse‐grained ones values between 0.02 and 0.09. The electrical conductivity for the fine‐grained and the coarse‐grained material is and S cm−1, respectively.

Texture Evolution and Nanohardness in Cu-Nb Composite Wires.

Multifilamentary microcomposite copper-niobium (Cu-Nb) wires were fabricated by a series of accumulative drawing and bonding steps (ADB). The texture of the Cu matrix in these wires was studied using electron backscattered diffraction (EBSD) and transmission electron microscopy (TEM). Dynamic recrystallization during cold drawing caused a weakening of the <111> texture in the micron-scale Cu matrix at high values of true strain. A sharp <111> texture was observed in the nano-scale Cu matrix due to the suppression of dynamic recrystallization. The grain size was reduced by the higher level of dynamic recrystallization at high strains. The relation between the nanoindentation behavior of the different Cu matrix and the grain sizes, Cu-Nb interface, and texture was established.

On Characteristics of Ferritic Steel Determined during the Uniaxial Tensile Test.

Tensile uniaxial test is typically used to determine the strength and plasticity of a material. Nominal (engineering) stress-strain relationship is suitable for determining properties when elastic strain dominates (e.g., yield strength, Young’s modulus). For loading conditions where plastic deformation is significant (in front of a crack tip or in a neck), the use of true stress and strain values and the relationship between them are required. Under these conditions, the dependence between the true values of stresses and strains should be treated as a characteristic—a constitutive relationship of the material. This article presents several methodologies to develop a constitutive relationship for S355 steel from tensile test data. The constitutive relationship developed was incorporated into a finite element analysis of the tension test and verified with the measured tensile test data. The method of the constitutive relationship defining takes into account the impact of high plastic strain, the triaxiality stress factor, Lode coefficient, and material weakness due to the formation of microvoids, which leads to obtained correctly results by FEM (finite elements method) calculation. The different variants of constitutive relationships were applied to the FEM loading simulation of the three-point bending SENB (single edge notched bend) specimen to evaluate their applicability to the calculation of mechanical fields in the presence of a crack.

Effects of Austenitization Temperature and Pre-Deformation on CCT Diagrams of 23MnNiCrMo5-3 Steel.

The combined effect of deformation temperature and strain value on the continuous cooling transformation (CCT) diagram of low-alloy steel with 0.23% C, 1.17% Mn, 0.79% Ni, 0.44% Cr, and 0.22% Mo was studied. The deformation temperature (identical to the austenitization temperature) was in the range suitable for the wire rolling mill. The applied compressive deformation corresponded to the true strain values in an unusually wide range. Based on the dilatometric tests and metallographic analyses, a total of five different CCT diagrams were constructed. Pre-deformation corresponding to the true strain of 0.35 or even 1.0 had no clear effect on the austenite decomposition kinetics at the austenitization temperature of 880 °C. During the long-lasting cooling, recrystallization and probably coarsening of the new austenitic grains occurred, which almost eliminated the influence of pre-deformation on the temperatures of the diffusion-controlled phase transformations. Decreasing the deformation temperature to 830 °C led to the significant acceleration of the austenite → ferrite and austenite → pearlite transformations due to the applied strain of 1.0 only in the region of the cooling rate between 3 and 35 °C·s−1. The kinetics of the bainitic or martensitic transformation remained practically unaffected by the pre-deformation. The acceleration of the diffusion-controlled phase transformations resulted from the formation of an austenitic microstructure with a mean grain size of about 4 µm. As the analysis of the stress–strain curves showed, the grain refinement was carried out by dynamic and metadynamic recrystallization. At low cooling rates, the effect of plastic deformation on the kinetics of phase transformations was indistinct.

Weibull S-N Fatigue Strength Curve Analysis for A572 Gr. 50 Steel, Based on the True Stress—True Strain Approach

In this paper a Weibull methodology to determine the probabilistic percentiles for the S-N curve of the A572 Gr. 50 steel is formulated. The given Weibull/S-N formulation is based on the true stress and true strain values, which are both determined from the stress-strain analysis. For the analysis, the Weibull β and η parameters are both determined directly from the maximum and minimum addressed stresses values. The S-N curve parameters are determined for 103 and 106 cycles. In the application, published experimental data for the CSA G40.21 Gr. 350W steel is used to derive the true stress and true strain parameters of the A572 Gr. 50 steel. Additionally, the application of the S-N curve, its probabilistic percentiles and the Weibull parameters that represent these percentiles are all determined step by step. Since the proposed method is flexible, then it can be applied to determine the probabilistic percentiles of any other material.

Determination of true stress-strain curve of type 304 and 316 stainless steels using a typical tensile test and finite element analysis

Knowing a material’s true stress-strain curve is essential for performing a nonlinear finite element analysis to solve an elastoplastic problem. This study presents a simple methodology to determine the true stress-strain curve of type 304 and 316 austenitic stainless steels in the full range of strain from a typical tensile test. Before necking, the true stress and strain values are directly converted from engineering stress and strain data, respectively. After necking, a true stress-strain equation is determined by iteratively conducting finite element analysis using three pieces of information at the necking and the fracture points. The Hockett-Sherby equation is proposed as an optimal stress-strain model in a non-uniform deformation region. The application to the stainless steel under different temperatures and loading conditions verifies that the strain hardening behavior of the material is adequately described by the determined equation, and the estimated engineering stress-strain curves are in good agreement with those of experiments. The presented method is intrinsically simple to use and reduces iterations because it does not require much experimental effort and adopts the approach of determining the stress-strain equation instead of correcting the individual stress at each strain point.

Strain rate and temperature dependent strain localization of a near α titanium alloy

The tensile response of a near α Ti3Al2.5V alloy, conceived for jet engine fan containment applications, is characterized by Digital Image Correlation (DIC) technique at quasi-static 0.001 s−1, medium rate 12 s−1 and high strain rates 700 s−1-3000 s−1 at room temperature and elevated temperatures 100°C and 200°C. The material is found to present noticeable strain rate sensitivity. Observations indicate that the dynamic true strain rate in the necking cross-section can reach values up to 10,000 s−1 due to strain localization. True stress-strain relationship beyond necking at high strain rates presents limited rate dependent response, however, there is clearly no locking of strain rate effect from medium rate to high rates. A series of tests undertaken at elevated temperatures indicate that the higher temperature results in a higher true strain rate for corresponding values of true strain. Experimental results from quasi-static test condition to high strain rates are used to determine an appropriate constitutive model for finite element simulations of the tensile experiments. The model accurately predicts the experimentally dynamic macroscopic force-time response and local true stress-strain relationship, and reveals the increasing trend of true strain rate evolution and decreasing trend of dynamic amplification evolution in good agreement with the experimental measurements with the average absolute relative error less than 8.4 % and the Pearson correlation coefficient larger than 0.957.

Effect of Stress-Relieving Heat Treatment on the High Strain Rate Dynamic Compressive Properties of Additively Manufactured Ti6Al4V (ELI)

A study was undertaken on the compressive high strain rate properties and deformation behaviour of Direct Metal Laser-Sintered (DMLS) Ti6Al4V (ELI) parts in two separate forms: as-built (AB) and stress relieved (SR). The high strain rate compression tests were carried out using a Split Hopkinson Pressure Bar test system at ambient temperature. The average plastic strain rates attained by the system were 400 s−1 and 700 s−1. Comparative analyses of the performance (flow stresses and fracture strains) of AB and SR specimens were carried out based on the results obtained at these two plastic strain rates. Microstructural analyses were performed to study the failure mechanisms of the deformed specimens and fracture surfaces. Vickers microhardness test values were obtained before and after high strain rate compression testing. The results obtained in both cases showed the strain rate sensitivity of the stress-relieved samples to be higher in comparison to those of as-built ones, at the same value of true strain.

Structural Transformations in Copper during High-Speed Deformation upon the Convergence of a Massive Cylindrical Shell under Implosion

The deformation structure in copper that forms upon the convergence of a massive cylindrical shell into a cylinder is studied in this work. The shell in the deformation zone was subjected to high-speed deformation (~104 1/s) with large values of true strain (e varied from 0.8 to 2.0). It is shown that two types of structures were formed under deformation: regions containing disperse grains with high-angle boundaries and twins and regions with deformation cells having low-angle boundaries. It is found that the twins that arose at the early stages of deformation are distorted upon further deformation: their rectilinear boundaries are bent, the orientation relationships with the matrix are violated, and high-angle boundaries of arbitrary orientation are formed.

A numerical solution to accurately predict deformation behaviour of metallic foam material up-to densification region for the possible use in composite structures

Closed cell metallic foam material has immense potential to use it as core material in composite structures. In the design of such structures and to understand numerically its deformation behaviour there is a difficulty of choosing the correct constitutive behaviour of metallic foam due to its porous structure. A solution has been proposed to accurately predict the experimental behavior of a closed-cell metallic foam up-to densification region by the use of a crushable foam model under compressive loading condition. The effect of using different stress-strain material curves and other input parameters of the crushable foam model is quantified in terms of predicting experimentally determined compressive load-displacement behavior of the metallic foam. It has been found that for predicting accurate compressive behavior of metallic foam using a crushable foam model, the hardening behavior of metallic foam may be defined by engineering stress vs. true strain values.

Investigations on multi-sheets single point incremental forming of commercial pure titanium alloys

ABSTRACT The rate of production in single point incremental forming (SPIF) approach for the sheet metals is comparatively low when comparing to multiple sheet incremental forming process (MSSPIF). This increase in production rate comes with a trade-off of reduced formability in MSSPIF. The aspiration of the current paper is to analyze the formability, the strain distribution, and the void coalescence variables as per the strain triaxiality during the MSSPIF process of the available commercially pure (CP) titanium sheets. The forming limit diagrams (FLDs) and the strain distribution analysis have been carried out for multiple sheets of two, three, and four sheets bunch while they were formed together. The outcomes proved that the uppermost sheets achieved the higher limiting principal true strain and the limiting values of the principal true strain of bottom sheets decreased in accordance with the position of the sheet and the same was reported in FLDs. The void coalescence in the fractured specimen exhibited an enhanced fracture resistance for CP sheets of titanium. The size of void (µm), thickness of ligament (LT), void (L/W) ratio, d-factor, strain triaxiality, and other void coalescence parameters also have been compared when two, three, and four sheets were formed together during MSSPIF process.

Enhancement of fracture forming limit by crystallographic texture reformation of AA1050 sheets in Single Point Incremental Forming

Single Point Incremental Forming (SPIF) process that results in the formation of sheet metal components leads to higher forming capabilities in comparison to conventional forming strategies. However, the formability in SPIF is critical and limited by the rapid/sudden failure in the sheet material (without material localization) for the components with high wall inclination angles. The state of stresses and strains plays a huge role in determining the forming limits in SPIF, which is complexly governed by various factors such as sheet thickness, lubrication, incremental step depth, tool rotational speed, part geometry, tool dimensions, and geometry, to name a few. The present work focuses on investigating formability of the sheets from its microstructure and crystallographic texture point of view. Preliminary experimentation led to the conclusion that SPIF of the original commercially supplied AA1050 H14 sheets results in early and premature failure. Microstructural investigation of the undeformed sheet showed that the commercially supplied sheets undergo strain hardening due to cold rolling and therefore, results in dislocated and disorientated microstructure and texture. The present work attempts to reform the microstructure of the sheet by preheating at the optimized temperature. Finite element analysis (FEA) of the process led to the observation that the reformed microstructures result in enhanced fracture forming limit strain and reduced stresses in SPIF. This may be attributed to the decrease in the number of dislocations and dislocated grains, and decrease in the surface area of grain boundary per grain with preheating. Improved fracture forming limits due to preheating were experimentally validated by utilizing digital image correlation technique (DIC) for acquiring true strain values subjected to fractured original and different preheated samples.

Hot Flow Curve Description of CuFe2 Alloy via Different Artificial Neural Network Approaches

In this research, a mathematical description of hot flow curves of CuFe2 copper alloy has been assembled. Experimental flow curves of the investigated alloy were created on the basis of hot compression dataset. This dataset was acquired in the temperature range of 923-1223 K and the strain rate range of 0.1-10 s−1, with the maximum true strain value of 1.0. The experimental flow curves were described by two artificial neural network approaches. In the first case, a neural network has been created to approximate the experimental flow curves with respect to the true strain, strain rate and temperature. In the second case, a hybrid approach based on the combination of predictive models with neural networks has been utilized. In this case, five neural networks were used to describe parameters of these models in relation to the temperature and strain rate. Results have shown that the hybrid approach allows an accurate description of the experimental data and also provides more reliable prediction.

Effect of Processing Routes on Orientation-Dependent Tensile Flow Behavior of Zircaloy-4 at Elevated Temperatures

The present work describes the correlation between orientation-dependent tensile flow behavior and texture of Zircaloy-4 sheet at elevated temperatures. The sheets are manufactured from three different routes, namely slab route, tube route, and pilgering. The material is tested at elevated temperatures raising from 75 to 225 °C with an increment of 75 °C. The XRD results show that the texture intensity is more in LOS than that of the other two. In all the three alloys, irrespective of temperature, the yield strength is maximum in transverse direction and minimum in longitudinal direction. The yield strength dependent in-plane anisotropy (AIP) and percent of elongation-dependent anisotropy (δ) values show presence of moderate textures. The true stress and true plastic strain values are best fitted with the Holloman equation, and the coefficient of determination (R2) ranges between 0.99039 and 0.99959. The differential curves are plotted by numerically differentiating true stress with respect to true plastic strain for quantitative description of work-hardening rate of materials. The differential curves of all the three alloys exhibit the three typical work-hardening regions (i.e., elasto-plastic transition, easy glide stage, dynamic recovery).