An implicit integration scheme with consistent tangent modulus for Leblond’s model of transformation-induced plasticity in steels

Thermomechanical treatments involving solid-state phase transformations play an important role for the manufacturing of functional and reliable components in many engineering applications. Accordingly, numerical investigation and optimization of such processes require considering thermoelastoplasticity under the influence of ongoing transformations and in particular the impact of transformation-induced plasticity (TRIP). While a number of elaborate plasticity models have been proposed for the description of TRIP, none of them seem to have received much prevalence in applications due to their complexity or hard to determine model parameters. Instead, the overwhelming majority of applied research either relies on simplistic formulations dating back to early phenomenological approaches or neglects TRIP altogether. In this work, we therefore provide an accessible, straightforward and easy-to-implement solution scheme for the TRIP model proposed by Leblond et al. which, despite being widely recognized, is hardly ever employed in full form. Specifically, we employ implicit backward-Euler integration and an elastic–plastic operator split approach to update the stresses in order to obtain a simple and concise algorithm for which we then derive the corresponding consistent tangent modulus. Furthermore, the work contains an application of the solution scheme to a symmetrically cooled plate and an in-depth discussion of the influence of TRIP by means of this tractable numerical example. Specifically, we highlight the discrepancies arising in transient and residual stresses and strains compared to the conventional $$J_2$$ J 2 -plasticity approach where the phase transformation is accounted for merely by adapting the yield strength of the compound.

Effects of temperature gradient on the granite’s mechanical properties

Temperature gradient significantly affects the production of surrounding rock stress in mining engineering. The mechanics and deformation characteristics of the rock will change under the temperature gradient, thereby increasing the probability of accidents in the roadway. This paper conducts uniaxial compression tests on granite at different temperatures from room temperature to 250∘C, and analyzes in detail the changes in the stress-strain curve, peak stress, peak strain and tangent modulus of granite under high temperature and different temperature gradient conditions. The results of this study are as follows: (1) Under high temperature conditions, the granite’s peak stress and tangent elastic modulus increased with temperature from 17 to 100∘C, then decreased from 100∘C to 250∘C, whereas the granite’s peak strain increased steadily with increasing temperature; (2) under temperature gradient, the granite’s peak stress and tangent modulus first decreased and then increased with increasing temperature gradient, while the granite’s peak strain first decreased and then increased at 100∘C, but first increased and then decreased from 150∘C to 250∘C.

Experimental Investigation of the Effects of High Temperature Treatment on Quasi-Static Mechanical Characteristics of EMWM Materials

This paper investigates the influence of high temperature treatment processes on the mechanical characteristics of entangled metallic wire materials (EMWM) via quasi-static compression tests. The treatment methods including high-temperature treatment and high-temperature with loading treatment were tested. The variation effects of size in molding direction, tangent modulus and loss factor were obtained by contrast results of EMWM specimens via the treatment processes with initial performance. The results indicate that the treatment processes proposed in this study can significantly improve the mechanical properties of EMWM materials and have a wide range of application for EMWM specimens with different structural parameters. After the treatment processes, the size of specimens in molding direction decreased slightly, the tangent modulus increased significantly, and the loss factor decreased slightly. With the increase of treatment temperature, the variation of mechanical parameters intensified. For EMWM specimens with different relative densities and heights, the treatment processes still have a significant improvement effect on quasi-static mechanical properties. Finally, the secondary molding theory is carried out to explain the influence of high temperature treatment process on EMWM’s dimensions and mechanical properties. The effects of treatment temperature and repetition times obtained in this study are relevant to the design of treatment processes for EMWM materials.

Study on the Influence of Different Prophase Stress Levels on the Fatigue Damage Characteristics of Granite

In order to reveal the influence of prophase stress levels on the fatigue damage characteristics of granite, uniaxial fatigue tests of granite with different prophase stress levels were carried out on the basis of the MTS 815.04 rock mechanics test system. The results show that, under the same number of cycles, the failure degree increases with the increase of the prophase stress level. Under the low upper limit of cyclic stress, the tangent modulus and dissipated energy increase significantly with the increase of prophase stress level at the early stage of the cycle loading, while the increasing trend is not obvious with the increase of prophase stress level at the late stage. Under the high upper limit of cyclic stress, the tangent modulus and dissipated energy are less affected by the prophase stress level. The development trend of elastic release energy is not obvious with the increase of prophase stress level, which is less affected by the number of cycles. From the damage parameters defined by dissipative energy, under the low upper limit of cyclic stress, the initial damage is less affected by the prophase stress level. With the increase of the number of cycles, the influence of the prophase stress level on the development trend of the damage variable increases gradually. And the development trend of damage variables shows “C-shaped” damage.

In Vitro Effect of the Biomechanics After Photodynamic Therapy (PDT) Intervention on Rabbit Cornea

Objective: To observe the change of the biomechanical properties of rabbit cornea after the intervention by corneal collagen cross linking (CXL) and toluidine blue O combined with red light (TBOR).Methods: The study was carried out in compliance with the ARRIVE guidelines. 20 healthy adult New Zealand white rabbits were randomly divided into two groups. One group was taken with Riboflavin combined with UV light therapy in the right eye of healthy New Zealand white rabbits, and the other group was taken toluidine blue O combined with red light (TBOR) treatment. All left eyes were taken as controls. Parameters, from Pentacam and Corvis ST like K1 (The keratometry readings of the flattest), K2 (The keratometry readings of the steepest), ACD (Anterior chamber depth), Pupil diameter, ACA (Mean angle of the anterior chamber), ACV (Volume of the anterior chamber), bIOP (Biomechanical Intraocular pressure), CT (Corneal thickness, pachymetry), A1 Time(Time from starting until the first applanation), A1 Velocity(Corneal speed during the first applanation moment), A2 Time (Time from starting until the second applanation), A2 Velocity (Corneal speed during the second applanation moment), HC Time(Time from starting until highest concavity is reached), Peak Dist(Distance of the two “peaks” at highest concavity) and HC-Radius(The radius at highest concavity), were examined before and 2 weeks after intervention. The rabbits were sacrificed after anesthesia. Then, their corneas were removed for corneal stretch test.Results: With the examination of Pentacam and Corvis ST, IOP(11.28 ± 11.2mmHg v.s. 6.66 ± 4.02mmHg) and A1 time(7.03 ± 1.27s v.s. 6.55 ± 0.35s) were increased, comparing with those before intervention. From the in vitro corneal stretch test, the tangent modulus of the CXL group was more than 3 times of the Control group, whereas the tangent modulus of the TBOR group was about 0.7 times to that of the Control group.Conclusions: From the rabbit cornea intervention with CXL and TBOR, CXL showed an obvious effect of increasing the hardness of rabbit cornea, while TBOR may did no help to increase the hardness of cornea.

Effect of Achilles Tendon Mechanics on the Running Economy of Elite Endurance Athletes

The Achilles tendon stores and releases strain energy, influencing running economy. The present study aims to verify the influence of the Achilles tendon tangent modulus, as a material property, on running economy by comparing two groups of elite endurance-performance athletes undergoing different running training volumes. Twelve athletes, six long-distance runners and six pentathletes, were studied. Long-distance runners had a higher weekly running training volume (116.7±13.7 vs. 58.3±20.4 km, p<0.05) and a better running economy (204.3±12.0 vs. 222.0±8.7 O2 mL ∙ kg−1 ∙ km−1, p<0.05) evaluated in a treadmill at 16 km·h–1, 1% inclination. Both groups presented similar VO2max (68.5±3.8 vs. 65.7±5.0 mL ∙ min−1 ∙ kg−1, p>0.05). Achilles tendon tangent modulus was estimated from ultrasound-measured deformations, with the ankle passively mobilized by a dynamometer. True stress was calculated from the measured torque. The long-distance runners had a higher maximum tangent modulus (380.6±92.2 vs. 236.2±82.6 MPa, p<0.05) and maximum true stress than pentathletes (24.2±5.1 vs. 16.0±3.5 MPa, p<0.05). The correlation coefficient between tangent modulus at larger deformations was R=–0.7447 (p<0.05). Quantifying tendon tissue adaptations associated with different running training volumes will support subject and modality-specific workouts prescription of elite endurance athletes.

Laboratory Model Test to Explore the Bearing Mechanism of Composite Foundation in the Loess Area

Pile composite foundation can make good use of the bearing capacity of the soil and pile, which is widely used in the Chinese northwest loess area. However, the theory of pile composite foundation is far from sufficient, hindering its long-term development. Aiming at this problem, a laboratory model test of pile composite foundation in the loess area was conducted to explore the common working mechanism and variations of each bearing stage. Besides, the settlement of the single pile composite foundation was calculated by using the modified tangent modulus method, and the result was compared with the experimental data. The main results of this paper are as follows: Both in the single pile and single pile composite foundation, loading-settlement curves showed a trend of “elastic to elastoplastic to plastic,” accompanied by the appearance of plummeting point. Influenced by the pile group effect, the loading-settlement curve of the group pile composite foundation showed a slow-varying trend without an obvious breakdown point. Pile axis stress increased with the growth of upper load. At the beginning of loading, the pile axis stress indicated such a distribution that stress on both ends of the pile was larger than that in the middle of the pile. When reaching a certain load, the location of the biggest pile axis stress transferred to the pile top, and the pile axis stress decreased gradually as the pile became deep. The side friction resistance in the static load test of the single pile was always positive, whereas in the composite foundation of a single pile and a group of piles, negative side resistance appeared in the upper side of the neutral point. Pile-soil stress ratio in the depth of 12 cm changed with the upper load. The outcome calculated by the modified tangent modulus method had a relatively better consistency with experimental data if the upper load was not too large.

Effect of In Situ Grown BNNTs and Preparation Temperature on Mechanical Behavior of SiC/SiC Minicomposites

In this paper, effect of in situ grown boron nitride nanotubes (BNNTs) and preparation temperature on mechanical behavior of PIP (Precursor Infiltration and Pyrolysis) SiC/SiC minicomposites under monotonic and compliance tensile is investigated. In situ BNNTs are grown on the surface of SiC fibers using ball milling – annealing process. Composite elastic modulus, tensile strength, fracture strain, tangent modulus, and loading/unloading inverse tangent modulus (ITM) are obtained and adopted to characterize the mechanical properties of the composites. Microstructures of in situ grown BNNTs and tensile fracture surfaces are observed under scanning electronic microscopic (SEM). For SiC/SiC minicomposites with BNNTs, the elastic modulus, tensile strength, and fracture strain are all lower than those of SiC/SiC minicomposites without BNNTs, mainly due to high preparation temperature and the oxidation of the PyC interphase during the annealing process. Tensile stress-strain curves of SiC/SiC minicomposites with and without BNNTs are predicted using the developed micromechanical constitutive model. The predicted results agreed with experimental data. This work will provide guidance for predicting the service life of SiCf/SiC composite materials and may enable these materials to become a backbone for thermal structure systems in aerospace applications.