Dynamic Constitutive Relation Research Articles

Research on Dynamic Compressive Performance of Polypropylene Fiber-Reinforced High-Strength Concrete under Freeze-Thaw Environment

Existing studies have proved that the incorporation of polypropylene fiber can effectively improve the impact resistance of concrete. In this paper, the split Hopkinson pressure bar and digital pulse shaping technology are used to further study the dynamic compression performance and constitutive relationship of concrete in the cold regions under the deteriorating effect of freeze-thaw cycle, and obtain the dynamic increase factor. Studies have shown that polypropylene fiber-reinforced high-strength concrete has a strain rate enhancement effect. The number of freeze-thaw cycle times at low strain rates has an obvious effect on concrete deterioration, and the effect is weaker at higher strain rates. By comparing three typical dynamic strength growth factor models with the test results, after revising the model, the dynamic increase factor equations under different freeze-thaw circulation times were fitted. This research provides a basis for the design of durability and robustness of building structures in cold regions.

A settlement prediction model considering tidal loading and traffic loading of soft soil subgrade

A large number of soft soil subgrade projects have been built in the tidal-flat zone of southeast China. Where, in addition to bearing the traffic loading, the soft soil subgrade may be swallowed up by tidal water. Therefore, the soft soil subgrade will bear long-term coupling action of tidal loading and traffic loading in the tidal-flat zone. Excessive settlement accidents of the subgrade occur frequently in the tidal-flat zone. In this study, a new dynamic constitutive relation considering seepage characteristics was used and the UMAT subroutine was embedded in ABAQUS. FE parametric analysis was analyzed considering three influencing factors of tidal amplitudes, traffic loading amplitude and tidal period. A multi-factor coupling settlement prediction expression considering tidal loading and traffic loading of soft soil subgrade suitable for soft soil subgrade in the tidal-flat zone was proposed. In addition, a settlement prediction program of soft clay subgrade under the combined tidal loading and traffic loading was designed and developed to facilitate engineering use. The research results can be applied to the subgrade projects in the tidal-flat zone, and provide a reference for engineering decision-making and disaster prevention and mitigation.

Dynamic tensile mechanisms and constitutive relationship in CrFeNi medium entropy alloys at room and cryogenic temperatures

Harsh service conditions in aerospace, defense and military, and other fields are calling for materials with excellent mechanical properties to undergo extreme deformation (such as elevated and cryogenic temperatures and high strain rates) without sustaining damage while retaining high strength. Outstanding mechanical properties of high or medium entropy alloys (MEAs) render them potential candidates. In this paper, as the temperature decreases, a breakthrough of the strength-ductility tradeoff is achieved in a CrFeNi MEA with partially recrystallized face-centered cubic phases, together with body-centered cubic (BCC) precipitates. At a strain rate of $3000\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, the yield strength (YS) is increased from 920 MPa at 298 K to 1320 MPa at 77 K, while the uniform elongation (UE) increases by 28.5%. This phenomenon also occurs at quasistatic tension. Under low-temperature loading, nanotwins are popularly activated due to the decreased stacking fault energy with decreasing temperatures. A positive strain-rate dependent YS arises owing to the contributions from the short-range dislocation obstacles, BCC phases, and refined grains. High-density dislocations and BCC phases result in the degeneration of UE, especially with the increase of strain rates. Strain-rate- and temperature-dependent constitutive models were successfully established to predict the deformation behaviors of CrFeNi MEAs under such a wide range of strain rates at room and cryogenic temperatures.

Dynamic mechanical properties and comparison of two constitutive models for martensitic stainless steel 0Cr17Ni4Cu4Nb

The purpose of the study is to investigate the dynamic mechanical properties and constitutive relationship of martensitic stainless steel 0Cr17Ni4Cu4Nb. For this purpose, the impact test was performed at six strain rates (750, 1500, 2000, 2600, 3500, and 4500 s−1) and four temperatures (25, 350, 500, and 650 °C) by using the high-temperature split Hopkinson pressure bar (SHPB) test device to attain the stress–strain relationship of materials; in addition, quasi-static (0.001, 0.01, and 0.1 s−1) compression tests were conducted by applying the UTM5305 universal testing machine at normal temperature. The analysis of the stress–strain curves indicates that the stainless-steel shows strain-rate strengthening and thermal softening and the adiabatic temperature rise during the plastic deformation at a high strain rate exerts a thermal softening effect on materials. With the aid of Johnson-Cook (J-C) and power-law (P-L) constitutive models, the dynamic constitutive relation of the martensitic stainless steel 0Cr17Ni4Cu4Nb was fitted and the correlation coefficients (R) and average absolute relative errors (AAREs) obtained through use of the two constitutive models were compared. Results indicate that the curves obtained through the constitutive models match the test curves to a reasonable extent. The R values are 0.968 33 and 0.977 80 while AAREs obtained through the J-C and P-L models are 4.77% and 2.25%, respectively. It can be found that the P-L model is slightly superior to the J-C model in terms of fitting accuracy. In addition, the dynamic mechanical properties of the materials were assessed through use of their constitutive equations from the perspectives of strain-rate sensitivity and temperature sensitivity and the acquired results are relatively consistent with the test results.

Dynamic Behavior and Constitutive Relationship of Mudstone Slip Zone of Landslide with Weak Interlayer

Sliding zone dynamics in the Qinling-Daba mountain area under different dynamic parameters have not been studied extensively. In this study, we investigated the dynamic behavior of the sliding zones of a high-steep rock landslide in the Qinling-Daba mountain area under the influence of dynamic stress amplitude and frequency and proposed an empirical model of the dynamic constitutive relationship. The dynamic behavior was studied based on a cyclic triaxial test system. The results indicated that an increase in the dynamic stress amplitude decreased the dynamic elastic modulus linearly, increased the damping ratio, and increased the axial strain exponentially. Among these properties, the elastic strain was found to be more sensitive to the increase in the dynamic stress amplitude than the plastic strain. As the loading frequency increased, the dynamic elastic modulus increased, whereas the damping ratio decreased. Furthermore, the proposed empirical model of the dynamic constitutive relationship between the vibration number and loading frequency based on the dynamic elastic modulus could satisfactorily describe the dynamic stress-strain relationships of the samples from test stability and failure zones. These findings are expected to make a significant contribution toward further revealing the sliding mechanism of such landslides.

Study on Dynamic Bond-Slip Constitutive Relation of Corroded Mortar Anchor

In order to study the bonding performance of corroded mortar anchor under dynamic load and reveal the mechanism of dynamic bond-slip, dynamic pull-out tests for mortar anchors with different corrosion degrees were carried out. On the basis of the average bond stress and relative slip, the basic bond-slip constitutive relation of corroded mortar anchor was established according to the measured data. The bond stress under different loading frequency were fitted, and the dynamic influence coefficient affecting the bond performance of mortar anchor was obtained. Based on the bond stress-slip relationship of each point in the anchorage section under different corrosion degrees, the position function in anchorage section was deduced. According to the above basic bond-slip relation, dynamic influence coefficient and anchorage position function, the dynamic bond-slip constitutive relation of corroded mortar anchor regarding to anchorage position was established, which could provide reference for the study on the durability of mortar anchor and its dynamic anchorage performance.

Dynamic Splitting Behavior and the Constitutive Relationship of Frozen Sandstone Containing a Single Fissure

Fractured sandstone is widely distributed in mining areas throughout western China where the artificial freezing method is extensively adopted to construct vertical shafts. Blasting and excavation generate stress waves and break frozen fractured sandstone. Among the failure modes of frozen fractured rocks, tensile failure is very common. In this study, the dynamic tensile strength of fractured sandstone samples with four crack inclination angles (0°, 30°, 60°, and 90°) is tested by using a split Hopkinson pressure bar at four subzero temperatures (−5, −10, −15, and −20°C). Accordingly, a damage constitutive relationship that considers the effect of fissure angle and freezing temperature is established. The results show the following: (1) the fissure angle does not significantly affect the dynamic tensile strength of frozen fractured sandstone but mainly affects the failure mode of the sample. (2) The dynamic tensile strength of fractured sandstone has a negative linear correlation with the freezing temperature. (3) When the fissure angle is small, only tensile cracking occurs; when the fissure angle is large, tensile cracking occurs along both the loading direction and the fissure; and shear cracking occurs along the fissure as well. (4) Regardless of the fissure angle, tensile cracking is initiated at the stress-concentration zone and then propagates towards the loading end. Fissure ice provides both resistance to deformation and resistance to crack propagation which affects the crack propagation and coalescence mode. A dynamic constitutive relationship is established by considering the effects of fissure angle and freezing temperature on the dynamic properties of frozen fractured sandstone, which is proven to be highly reliable and provides a reference and basis to study the dynamic mechanical properties of similar rock types.

Experimental Study on Biaxial Dynamic Compressive Properties of ECC.

An improved hydraulic servo structure testing machine has been used to conduct biaxial dynamic compression tests on eight types of engineered cementitious composites (ECC) with lateral pressure levels of 0, 0.125, 0.25, 0.5, 0.7, 0.8, 0.9, 1.0 (the ratio of the compressive strength applied laterally to the static compressive strength of the specimen), and three strain rates of 10−4, 10−3 and 10−2 s−1. The failure mode, peak stress, peak strain, deformation modulus, stress-strain curve, and compressive toughness index of ECC under biaxial dynamic compressive stress state are obtained. The test results show that the lateral pressure affects the direction of ECC cracking, while the strain rate has little effect on the failure morphology of ECC. The growth of lateral pressure level and strain rate upgrades the limit failure strength and peak strain of ECC, and the small improvement is achieved in elastic modulus. A two-stage ECC biaxial failure strength standard was established, and the influence of the lateral pressure level and peak strain was quantitatively evaluated through the fitting curve of the peak stress, peak strain, and deformation modulus of ECC under various strain rates and lateral pressure levels. ECC’s compressive stress-strain curve can be divided into four stages, and a normalized biaxial dynamic ECC constitutive relationship is established. The toughness index of ECC can be increased with the increase of lateral pressure level, while the increase of strain rate can reduce the toughness index of ECC. Under the effect of biaxial dynamic load, the ultimate strength of ECC is increased higher than that of plain concrete.

Dynamic mechanical response and a constitutive model of 42CrMo steel that incorporates the effects of high strain rates

<p indent=0mm>To study the dynamic mechanical properties and constitutive relationship of 42CrMo steel, which is primarily used in high-speed train axles, a dynamic compression test and a metallographic observation were conducted. The material exhibited strong strain-rate dependence, and the adiabatic shear behavior under dynamic loadings was found to be the dominant cause of the different mechanical properties resulting from different strain rates. The thermal activation theory, which separately considers the thermal and athermal stresses to explain the deformation mechanism, was employed to obtain the descriptions of the strain-rate effects. Accordingly, a physically based constitutive model was proposed that incorporated the effects of the high strain rates. A criterion for adiabatic shear, which was coupled to the model, was proposed to determine the onset of instability. The model was confirmed to sufficiently describe the quasi-static and dynamic mechanical behavior of the 42CrMo steel, especially the effects of strain hardening and strain rates on the yield stress.

Experimental study on dynamic stress dynamic strain relationship and dynamic modulus of reinforced expansive soil

Dynamic triaxial tests are carried out on saturated expansive soil of Qinchong Road, Guangxi at different compaction degrees, numbers of reinforced layers, confining pressure, dynamic stress dynamic strain relationship, and dynamic modulus attenuation law under frequency combination to study the dynamic characteristics of reinforced saturated expansive soil under different influencing factors. Results show that the dynamic constitutive relationship of the saturated expansive soil when the loaded waveform is a half-sine wave conforms to the R. L. Kondner hyperbolic model; the dynamic elastic modulus decreases with the increase of dynamic strain, and the relevant fitting parameters are given. A dynamic elastic modulus attenuation model considering different degrees of compaction, numbers of reinforced layers, confining pressure, and frequency is proposed through regression analysis of the test results.

Dynamic constitutive behavior investigation of a novel low alloy ultra-high strength steel

The goal of this work is to reveal the dynamic mechanical properties and constitutive relationship of a novel low alloy ultra-high strength DT506 steel under high strain rates. The quasi-static state and dynamic compression behavior of the material at the strain rates of 10−3–103 s−1 were examined using an MTS landmark electro-hydraulic servo universal tester and a Split-Hopkinson bar (SHPB). The results show that DT506 steel is a strain-rate-sensitive material that shows an increase in strength with increasing strain rate. Based on the quasi-static and dynamic compression data, the parameters in the Cowper-Symonds (C-S) and the Johnson-Cook (J-C) models are determined. Since the previously developed models are cannot accurately predict the effect of the strain rate. A new theoretical model is obtained through the optimization of the parameters in the standard J-C model. The optimized model greatly improves the prediction accuracy of the true stress-strain dynamic behavior of materials. This new model is helpful for the verification of the underlying mechanism of the dynamic behavior of the material. Test results may provide basic data for future research on dynamic mechanical properties and constitutive relationship of metal alloys.

Strain rate and temperature dependent strain localization of dynamically stretched lightweight bars: from metal to polymer

This work studies the dynamic strain localization and constitutive relationship of a Ti3Al2.5V alloy in jet engine containment system and a transparent polycarbonate conceived for aircraft canopy application by Digital Image Correlation (DIC) technique from quasi-static condition to high strain rates at different temperatures. The responses of two materials show significant strain rate and temperature sensitivities. Observations of Ti3Al2.5V alloy show that the dynamic local strain rate can reach values up to 1000 % of the nominal strain rate in the necking zone. However, dynamic local strain rate of polycarbonate soars up during strain softening then decreases rapidly with necking propagation, and eventually becomes 20 % of the nominal strain rate until fracture. Appropriate viscoplastic constitutive models are determined for both materials, which are incorporated in finite element simulations to reveal the trend of dynamic local strain rate evolution in dynamic tensile tests. The present work shows two different kinds of strain localization in typical lightweight materials, which should be addressed carefully from Split Hopkinson Tension Bar (SHTB) tests.

非均匀准脆性岩土类材料的动态力学本构关系的繁衍与演化

非均匀准脆性岩土类材料的动态力学本构关系的繁衍与演化

Dynamic Properties Test and Constitutive Relation Study of Lightweight Aggregate Concrete under Uniaxial Compression

For the purpose of studying the dynamic properties of lightweight aggregate concrete, dynamic performance tests under uniaxial compression were conducted by considering 10 different strain rates ranging from 10−5/s to 10−1/s, from which the stress‐strain curves under various compressive loads were obtained. From the stress‐strain curves, parameters including peak stress, peak strain, and elastic modulus of lightweight aggregate concrete, as well as the concrete failure mode, were determined and examined. By reviewing the relevant literature on ordinary concrete, the dynamic properties of lightweight aggregate concrete were analyzed accordingly. Meanwhile, by applying the dynamic elastoplastic damage constitutive model, the effect of dynamic rate on lightweight aggregate concrete was calculated. The experimental results showed that the damage mode of lightweight aggregate concrete under the static and dynamic strain rates belonged to shear failure, which is different from that of ordinary concrete (binding material failure). On the other hand, it was also found that the peak stress and elastic modulus of lightweight aggregate concrete could be increased by 54.48% and 28.75%, respectively, with the increase of strain rate, suggesting that the loading strain rate has a stronger influence on lightweight aggregate concrete than on ordinary concrete. Based on the experimental data, both the peak stress and nondimensionalized elastic modulus are in linear relationship with the logarithm of the nondimensionalized strain rate. Moreover, the established constitutive model had been verified as an effective and reliable tool for simulating the dynamic rate effect of lightweight aggregate concrete.

A simple elastoplastic dynamic constitutive model of saturated structural soft clay

The dynamic constitutive relation of soil is widely applied to the ground design of marine structure and infrastructure in offshore geotechnical engineering. Increasing evidence from marine geotechnical design has shown that the traditional dynamic constitutive model has uncertain theories, many parameters, and complexity. Therefore, it is urgent to overcome these limitations and develop a simple and practical elastoplastic dynamic constitutive relation for the saturated structural soft clay. A simple dynamic constitutive relation with 5 parameters was proposed in this study, which can reflect the strain accumulation, hysteretic characteristics and cyclic degradation of the stress-strain for structural soft clay. First, the Drucker-Prager model was selected as the bounding surface, hardening modulus equation was established by the hardening law, interpolation function and structural strength coefficient. Then, the incremental stress-strain relationship was derived based on the incremental theory. The UMAT subroutine was compiled by FORTRAN language. Finally, the cyclic triaxial test and numerical simulation were carried out, and the stress-strain relationship was analyzed. The research results showed that the test results were in good agreement with the prediction results of the model.

Dynamic Mechanical Properties and Visco-Elastic Damage Constitutive Model of Freeze-thawed Concrete.

To study the dynamic mechanical characteristics and constitutive relation of concrete materials under freeze–thaw (FT) cycle conditions, C35 concrete was taken as the research object in this paper, and FT tests were carried out with a freeze–thaw range of −20–20 °C and a freeze–thaw frequency up to 50 times. By using the separated Hopkinson pressure bar (SHPB) system, impact compression tests of concrete specimens under different FT cycle actions were developed, then the dynamic fracture morphology, fracture block distribution, stress–strain curve, peak stress and other dynamic mechanical properties of concrete were analyzed, and the influence law of FT action and strain rate was obtained. Through introducing the freeze–thaw deterioration damage factor and the stress damage variable, the dynamic visco-elastic damage constitutive equation of freeze–thawed concrete was constructed based on component combination theory. Furthermore, the damage evolution process and mechanism of freeze–thawed concrete materials were revealed. The research results show that the dynamic mechanical properties of concrete under a freeze–thaw environment are the combined results of the freeze–thaw deterioration effect and the strain rate strengthening effect. The dynamic visco-elastic damage constitutive model established in this paper can effectively describe the dynamic mechanical properties of freeze–thawed concrete, and has the characteristics of few parameters and good effect. The stress damage evolution path of concrete goes backward with the increase of FT cycles and the development speed gradually slows down. The greater the difference in FT cycles, the greater the difference in stress damage path.

Study on Dynamic Constitutive Model of Weakly Consolidated Soft Rock in Western China

To obtain the impact mechanical response and establish the dynamic damage constitutive relationship of frozen sandstone at low temperature conditions, the impact test of Cretaceous red sandstone under different temperatures was conducted using a split Hopkinson pressure bar (SHPB) device. According to the characteristics of the stress-strain curves obtained by the test, a constitutive model considering the damage effect, temperature effect, and strain rate effect was established, which was improved by Zhu–Wang–Tang (Z–W–T) constitutive model. It was proved that the fitting curves of constitutive equation were in good agreement with the test curves. The fluctuation amplitude of fitting error was controlled within ±4 MPa. The physical meaning of each parameter of the constitutive model is clear, and most of them are fixed values. The selection range of variable parameters and the related change rules are confirmed, which improves the practicability of constitutive model. The constitutive equation can well describe the nonlinear features of this kind of frozen sandstone under impact loading. It was also found that the constitutive equation was applicable to express the dynamic mechanical properties of rock-like materials such as hard rock, soft rock, frozen soil, raw coal, and concrete. It can be referred to the parameter determination method in this paper to study and determine the parameters, reduce the difficulty of parameter selection, and improve the practicability of the constitutive model and parameters, so as to guide the engineering practice better.

An Experimental Study of Dynamic Compression Performance of Self-Compacting Concrete.

To investigate the dynamic performance of self-compacting concrete (SCC), the dynamic uniaxial compression tests at eight different loading strain rates were performed on the ordinary concrete and SCC cubic specimens. Based on the tests, the compression failure patterns and stress–strain curves of both kinds of concrete were obtained. The results show that SCC performs more brittle than ordinary concrete by showing the diagonal crack failure pattern of SCC at a high strain rate. Besides, with the increase of loading strain rate, the peak compressive stress of SCC is slightly lower than that of ordinary concrete, but the increase of elastic modulus is slightly higher than that of ordinary concrete. The peak compressive strains of the two kinds of concrete are discrete under the influence of loading strain rate, thus putting forward the relation equation for the loading strain rate and peak compressive stress increase coefficient of the two kinds of concrete. Besides, based on the theory of elastic–plastic damage and considering the dynamic extension of damage, the dynamic constitutive relation with good applicability between ordinary concrete and SCC was established.

Dynamic constitutive relationship of CuCrZr alloy based on Johnson-Cook model

Abstract CuCrZr alloy has been acknowledged as one of the most promising candidate materials for the heat sink of plasma facing components in nuclear fusion devices with its excellent thermal conductivity and specific mechanical strength. For the safety concern, it is vital to provide appropriate safety assessment on these mechanical structures with CuCrZr alloy, such as divertor and blanket, under high strain rate loading conditions like displacement events, disruption, and so on. In this work, the dynamic compressive behavior of the CuCrZr alloy over wide range of strain rates and temperatures was investigated using the split Hopkinson pressure bar technique. Based on the experiment results, a constitutive equation is built by using Johnson-Cook model to describe the dynamical property of CuCrZr alloy. However, the results indicated that the influences of the strain, strain rate and temperature on the dynamic behavior are not independent. Therefore, a modified Johnson-Cook model was further developed to take the coupled effects of strain, strain rate and temperature into account. Compared with the original Johnson-Cook model, the modified Johnson-Cook model calculated results show good agreement with the experimental data.

Mechanical properties and dynamic constitutive relation of lightweight shale ceramsite concrete

To study the strength increasing rule of LWSCC in the process of freezing construction, some specimens were placed in cryogenic boxes at different subzero temperatures for curing, and the others were used as a control group for standard curing. After standard curing for 28 days, the specimens were placed in cryogenic boxes at different subzero temperatures for 1 day, and then the specimens were subjected to quasi-static loading and split Hopkinson pressure bar (SHPB) dynamic impact tests. Results showed that LWSCC had a stronger anti-freezing ability than the ordinary concrete and the strength growth was sensitive to the curing temperature. As the curing temperature decreased, the increasing rates of the compressive and tensile strengths became slow. The quasi-static and dynamic mechanical experiments showed that the strength of LWSCC was substantially enhanced when subjected to cryogenic temperatures after standard curing. Cryogenic LWSCC exhibited an obvious strain rate effect and impact resistance. A two-factor incremental model of the dynamic stress intensity factors and the dynamic constitutive equation of LWSCC in cryogenic temperatures were constructed. The conclusions obtained in the study provide a theoretical basis for the design of impact-resistant structures in cold areas.