An Inverse Piecewise Flow Curve Determination Method for Torsion Tests at Elevated Temperature

Indentation is widely used to investigate the elastic and plastic properties of mechanical materials, which includes the strain rate sensitivity. The indentation exhibits an inhomogeneous strain distribution in contrast to compression and tensile tests with homogeneous deformation. Thus, the strain rate of the indentation may form the inhomogeneous distribution. Therefore, the effect of strain rate distribution of the indentation on pure aluminum with respect to the strain rate dependence of strength in order to clarify the effect of the strain rate on the indentation technique. First, the numerical simulation was established using the Cowper-Symonds equation as the dynamic constitutive equation. Secondary, the strain rate distribution was calculated from the equivalent plastic strain distribution. The strain rate distribution was quite different from the strain distribution, which showed that the strain rate at the crater rim was higher than that beneath the indenter. Finally, we try to perform the averaging of strain rate distribution in order to make an index of strain rate in the indentation. The average of strain rate distribution was calculated using the equivalent plastic strain above a boundary value that is the critical strain and the representative strain. There is correlation between the average strain rate and the loading curvature, which shows that the average strain rate can express as the representative of strain rate for the indentation technique.

The design of industrial hot metal forming processes nowadays is mostly carried out using commercial Finite Element (FE) software codes. For precise FE simulations, reliable material properties are a crucial factor. In bulk metal forming, the most important material property is the materials flow stress, which determines the form filling and the necessary forming forces. At elevated temperatures, the flow stress of steels is determined by strain hardening, dynamic recovery and partly by dynamic recrystallization, which is dependent on strain rate and temperature. To simulate hot forming processes, which are often characterized by rapidly changing strain rates and temperatures, the flow stress is typically derived from flow curves, determined at arbitrary constant temperatures and strain rates only via linear interpolation. Hence, the materials instant reaction and relaxation behavior caused by rapid strain rate changes is not captured during simulation. To investigate the relevance of the relaxation behavior for FE simulations, trails with abrupt strain rate change are laid out and the effect on the material flow stress is analyzed in this paper. Additionally, the microstructure evolution due to the strain rate change is investigated. For this purpose, cylinder compression tests of an industrial case hardening steel are conducted at elevated temperatures and different strain rates. To analyze the influence of rapid strain rate changes, changes by one power of ten are performed at a strain of 0.3. As a reference, flow curves of the same material are determined at the initial and final constant strain rate. To investigate the microstructure evolution, compression samples are quenched at different stages, before and after the strain rate change. The results show that the flow curves after the strain rate change tend to approximate the flow curves measured for the final strain rate. However, directly after the strain rate change significant differences between the assumed instant flow stress and the real material behavior can be observed. Furthermore, it can be shown that the state of dynamic recrystallization at the time of the strain rate change influences the material response and relaxation behavior resulting in different slopes of the investigated flow curves after the strain rate change.

The work hardening behavior of metals subjected to strain path changes is different from that in monotonic deformation. Such changes can also lead to transients in flow stress and in the strain hardening rate. The origin of these phenomena is the instability of the dislocation structure produced during the initial straining. Subsequent deformation under a different path involves a restructuring of the dislocations [1]. The effect of a change in the strain path on the behavior of prestrained aluminum alloys was studied by Wilson et al. [2]. Decreased or enhanced work hardening rates were observed at the beginning of the second stage of deformation. These effects were associated either with the reorientation of internal stresses or to the dissolution of the original dislocation structure and the formation of a new one. Vieira and Fernandes [3] studied the influence of a double change in the strain path on the flow curve of copper sheets. The overall behavior depended more on the orientation relationship between the previous and the subsequent stage and less on the sequence of deformation. A high initial flow stress was usually followed by a low work hardening rate. The dislocation structure tended to correspond to the last mode of deformation. A transient flow behavior can also be caused by a change in the strain rate. The association of changes in the strain path and in the strain rate was investigated by Bate [4]. The effect of a strain rate change on the work hardening of aluminum samples was cancelled when a large change in the deformation mode was imposed. The elimination of the rate sensitivity was associated with the disruption of the cell walls due to a change in the strain path. The effects of a change in the strain path were evaluated in tension and torsion tests in this paper. The experiments were conducted in two and three stages and the results were compared with the flow curves from monotonic experiments. The material was a low carbon steel (0.245%C; 0.407%Mn; 0.155%Si; 0.0076%S). The torsion and tension specimens, 3.10 mm in radius (R) and 44.70 mm in length (L), were annealed in vacuum at 1000 ◦C for 20 min and furnace cooled to room temperature. The tests were performed at room temperature in a MTS servo hydraulic testing machine. The initial strain rate used in all experiments was 6.34× 10−2 s−1 [4, 5]. The samples were stored at∼−5 ◦C between two stages of deformation. Load (Q) and elongation (1L) were measured in tensile tests and torque (T ) and angle of twist (θ ) were measured in torsion tests. These data were converted into effective stress (σ ) and strain (e) using the following equations [6, 7]: Tension (uniform strain range):

In forming simulations, flow curves are cardinal inputs to predict features, such as forming forces and material flow. The laboratory-scale experiments to determine them, like compression or tensile tests, are affected by deformation heating, restricting direct flow curve determination. In principle, the current analytical and inverse methods determine flow curves from these tests, but while the analytical methods assume a simplified temperature profile, the inverse methods require a closed-form flow curve equation, which mostly cannot capture complex material behavior like multiple recrystallization cycles. Therefore, the inverse piecewise flow curve determination method “FepiM” previously developed and published by the current authors is extended by introducing a two-step procedure to obtain isothermal flow curves at elevated temperatures and different strain rates. Thereby, the flow curve is represented as tabular data instead of an equation to reproduce complex flow curve shapes while also compensating the effect of inhomogeneous temperature profiles on the flow stress. First, a flow curve at the highest temperature is determined. In the second step, using this first flow curve as a reference, the flow curves at lower temperatures are obtained via interpolation. Flow curves from conventional compression tests for aluminum and copper in the temperature range of 20–500 °C are predicted, and it is shown that these flow curves can reproduce the experimental forces with a maximum deviation of less than 1%. Therefore, the proposed new piecewise method accurately predicts isothermal flow curves for compression tests, and the method could be further extended to highly inhomogeneous methods in the future.

We constructed eight continuous GPS stations across the Nagamachi-Rifu fault zone, northeastern Japan to reveal the detailed spatial pattern of crustal deformation. High strain rate around the fault zone observed by the GEONET and the occurrence of the MJMA 5.2 Sendai earthquake on September 15, 1998, at the deep edge of the seismogenic part of the fault motivated us to confirm the aseismic sliding of the fault in or below the seismogenic depth from the contemporary deformation. We analyzed the GPS data of new stations as well as existing stations, totaling up to 50 stations in central Tohoku, using GIPSY 2.6.1 software and estimated GPS site velocity and strain rate by a least square method. One component of the principal strain rate shows distinctive compression in the E-W or ESE-WNW direction in the whole region. In the forearc region, the other component of the principal strain rate are almost zero in the south of 38°15′, while NNE-SSW extension in the north of 38°15′. Strain rate distribution is spatially heterogeneous in the region. We found a high strain rate zone west of the Nagamachi-Rifu fault zone and that between Honshu and Awashima in the eastern margin of the Sea of Japan. Low strain rate zones exist in the west of the high strain region of the Nagamachi-Rifu fault zone and in the western half of Yamagata Prefecture. Strain rate distribution pattern on the hanging wall side of the Nagamachi-Rifu fault can be modeled by aseismic sliding of 10mm/yr on a horizontal detachment fault connecting to the Nagamachi-Rifu fault at a depth of about 15km beneath the Ou backbone range. However, it is difficult to constrain a fault model for the strain rate distribution from the present dataset uniquely.

Interface tensile and fracture behavior of the Ti/Al3Ti Metal-Intermetallic Laminate (MIL) composite under quasi-static and high strain rates

In blast-induced caving mining with backfilling, understanding the interaction mechanisms and deformation evolution between rock and cemented tailing backfill (CTB) under coupled conditions is essential for ensuring stability. This study conducted dynamic uniaxial impact tests using the Split Hopkinson Pressure Bar (SHPB) system on rock-CTB composite specimens to investigate their mechanical response at high strain rates. Stress–strain relationships were recorded across a range of strain rates, and corresponding failure mechanisms were analyzed. A coupled SHPB model was also developed using GDEM software to simulate internal stress wave propagation and crack evolution within the composite specimens. Experimental results revealed that the dynamic compressive strength initially increases, then decreases, and eventually stabilizes as the average strain rate (ASR) increases from 27.45 s−1to 68.73 s−1. At strain rates below 60 s−1, the stress–strain curves exhibit a “stress drop” pattern, whereas above 60 s−1, a “stress rebound” behavior is observed. Energy absorption increases with ASR up to 55 s−1, then decreases, followed by a secondary increase. Numerical simulations validated the experimental findings, revealing the formation of both transverse and longitudinal cracks within the CTB. Greater deformation was observed near the transmission bar interface compared to the rock interface. These results offer valuable insights into the dynamic failure behavior of backfilled systems and inform improved backfill design in blast-induced mining operations.OPEN ACCESS Received: 05/08/2025 Accepted: 05/09/2025 Published: 03/02/2026

Hot tensile tests were carried out to investigate hot ductility behavior and critical temperature range (ΔT) between zero strength temperature (ZST) and zero ductility temperature (ZDT) of tool steel grades AISI L3 and O1. The test specimens solidified from melting at cooling rate of 0.5℃/s and 3℃/s to the test temperature in the range between liquidus and 900℃. The specimens were then strained to failure at strain rate of 2x10⁻³/s and 2x10⁻²/s. Quenching test was carried out in order to investigate the microstructure occurred during hot tensile test. The microstructure that appeared in quenched specimen was then identified with SEM-EDX. It was found that the critical temperature range of the steels solidified at the slow or the fast cooling rate, widened with increasing strain rate. The specimens which solidified at slow cooling rate when tensile strained to failure at low or high strain rate, had wider critical temperature range than the specimens that solidified at fast cooling rate. For steel grade AISI L3, tensile test at high and low strain rate (after solidified at the fast cooling rate) revealed the hot ductility of 35-65%RA between 900-1250℃. Whereas, the hot ductility of the samples which solidified at slow cooling rate and pulled at slow strain rate were markedly higher than those pulled at higher strain rate between 900-1200℃. Precipitation of manganese sulfide in the interdendritic region resulted in deterioration of hot ductility of steel grade AISI L3. For steel grade AISI O1, tensile tests of specimens solidified between 900-1100℃ at slow cooling rate and low strain rate yielded higher hot ductility than those specimens pulled at high strain rate. The hot ductility of samples at fast cooling rate and low strain rate showed no difference to those samples of hot tested at high strain rate. Nevertheless, slow cooling rate affected hot ductility more than fast cooling rate for tensile tests at both high and low strain rate. Carbide precipitates of vanadium, tungsten and chromium along austenite grain boundaries influenced the ductility loss of steel grade AISI O1.

To measure the flow stress of metals under forming conditions, i.e. at large strains, high strain rates and elevated temperatures, a method based on the ring compression test is proposed. In this method, a ring-shaped specimen is compressed between two flat tools with and without lubrication. The coefficient of friction between the specimen and the tools is determined from the change in inner diameter, and then the load and reduction in height measured in the test are converted into the average flow stress and average equivalent strain by taking the friction into account. The calibration curves for determining the coefficient of friction, the average equivalent strain and the average flow stress are derived from the results of rigid-plastic finite element calculation. This method is simple to carry out and does not require control of friction during compression. Ring compression tests for certain kinds of lubricants, materials and strain rates are carried out. The method is confirmed to provide flow curves within an error of 5%, and is effective especially for measuring the flow stress of heat-resistant materials such as Ti alloys and Ni base superalloys which are formed at elevated temperatures. As an example, the flow curves of Ti-6Al-4V alloy measured by the proposed method are demonstrated.

The effects of loading-direction and strain-rate on the mechanical behaviors of human frontal skull bone

The aim of this approach is to determine material characteristics of aluminium alloys at very high strain rates, in the form of a relationship between yield stress, plastic strain and strain rate. To achieve high strain rates up to 10 4 s -1 the electromagnetic forming process (EMF) is applied, where a pulsed magnetic field is used to form materials with a high electrical conductivity in process times between 20μs - 50μs. The forces resulting from the magnetic field and acting on the specimen, which in the considered setup is a tube, can be approximated as a time and location dependent pressure distribution. To compute the associated flow curve array, where the strain rate represents the third dimension, a new method will be proposed that combines an on-line measurement technique with iterative finite element simulations. During the electromagnetic compression of the specimen, the radial displacement of one significant point at the inner tube surface is measured on-line. These measured data are compared to the numerical results during the whole forming process and the deviations will be computed. Based on these differences an automated modification of material data is realised until the experimental data and the numerical solutions fit well. The advantage that EMF is a contactless forming process can be used to determine material characteristics without any influence of friction. Additionally, in contrast to other testing methods the assumption of a mean strain rate over the process time is not needed, because the evaluation is carried out by means of finite element simulations.

This article presents the results of analytical studies conducted using computer modeling in the QForm package. The influence of technological parameters of high-speed monolithic drawing on the stress-strain state and strain rate of the wire made of steel grade 10 was assessed. A billet with a diameter of 3.5 mm was drawn into a wire with a diameter of 3.0 mm through monolithic dies with a half-angle of 3; 4; 5; 6; 7 and 8° at a friction coefficient of 0; 0.05 and 0.10. The drawing speed was taken to be 10, 20, and 40 m/s. The analysis has established that increasing the value of the half-angle of the drawing leads to the occurrence of tensile stresses and strains in the surface layers of the wire. The value of the friction coefficient has a significant effect on the stress-strain state of the wire during drawing, increasing its value leads to increased unevenness of deformation along the section and increases the values and depth of penetration of tensile stresses and strains along the wire section. It has been established that the half-angle of the drawing die has a significant effect on the uniformity of the distribution of strain rates over the wire cross section. The maximum strain rate during drawing in monolithic dies can exceed twice the average strain rate. An increase in the die half-angle from 3 to 8° leads to an increase in the strain rate up to 2.5 times. The localization of high strain rates at large half-angles of wires with is concentrated in the central part of the wire. An increase in the drawing speed from 10 to 40 m/s leads to an increase in the strain rate up to 5 times. As a result of the research, it was shown that the QForm package is applicable for computer simulation of the drawing process in a monolithic die. The adequacy of the obtained results of the numerical experiment allows us to recommend it for conducting studies of the effect of technological parameters on the stress-strain state of wire of various assortment

Purpose – The aim of this paper was to investigate the effect of strain rate on microstructure and corrosion behavior of 2205 duplex stainless steel, after high-temperature compression tests. Design/methodology/approach – The specimens were prepared using a Gleeble3800 thermo-simulation machine over a range of temperatures from 850 to 1,250°C and strain rates from 0.005 to 5 s−1, and the corresponding flow curves and deformation microstructure obtained were further analyzed. To evaluate the effect of strain rate on corrosion behavior, potentiodynamic polarization tests and double-loop electrochemical potentiodynamic reactivation (DL-EPR) were used to characterize the electrochemical performance. Findings – Compared with strain rate of 0.5 s−1, the worst corrosion resistance behavior from the potentiodynamic polarization test results after deformation at 0.005 s−1 was attributed to more austenite (γ) and ferrite (δ) grain boundaries or δ/γ phase interface formation due to the better effect of γ dynamic recrystallization (DRX) or δ dynamic recovery (DRV). Increasing strain rate to 5 s−1 lowered the corrosion resistance, due to the increase in dislocation density. At the low strain rate of 0.005 s−1, the susceptibility to intergranular corrosion (IGC) was comparatively high after deformation at 1050 and 1150°C with more γ/γ grains and δ/γ phase boundary formation, which was lowered with the strain rate increase to 0.5 s−1, due to suppressing effect of γ DRX. Originality/value – The paper provides the scientific basis for the practical application of hot working of 2205 duplex stainless steel.

Strain rate dependency and fragmentation pattern of expanding warheads

In order to study the dynamic compression mechanical properties of engineering rock under high strain rate （100~102 S−1）loads, dynamic compression tests of three common engineering rocks (marble, sandstone and granite) taken from the Qinling Mountain are studied subjected to five different kinds of shock air pressure using Φ 100 mm split Hopkinson pressure bar test system improved with purple copper waveform shaper. The dynamic compression stress-strain curves, dynamic compressive strength, peak strain, energy absorption rate and elastic modulus of three rocks variation with strain rate are researched. The dynamic compression failure modes under different strain rates are analyzed. Then the three-dimensional numerical simulations of waveform shaper shaping effects and stress wave propagation in the SHPB tests are carried out to reproduce the test results. The research results show that the dynamic compression stress-strain curves show certain discreteness, and there is an obvious rebound phenomenon after the peak. With the increase in strain rate, the dynamic compressive strength, peak strain and energy absorption rate are all in a certain degree of increase, but the elastic modulus have no obvious change trend. Under the same strain rate, the dynamic compressive strength of granite is greatest while of sandstone is least. With the increase in strain rate, the margin of increase in peak strain and energy absorption rate of granite is greatest while of sandstone is least. The failure modes of the sample experience a developing process from outside to inside with the increase of strain rate.