• Advances in materials Research
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• v.12 no.1
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• pp.15-29
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• 2023

In this paper, fracture analysis of a continuously inhomogeneous arch structure with two longitudinal cracks is developed in terms of the time-dependent strain energy release rate. The arch under consideration exhibits non-linear creep behavior. The cross-section of the arch is a rectangle. The material is continuously inhomogeneous along the thickness of the cross-section. The arch is loaded by two bending moments applied at its end sections. The mechanical behavior of the material is described by using a non-linear stress-strain-time relationship. The two longitudinal cracks are located symmetrically with respect to the mid-span of the arch. Due to the symmetry, only half of the arch is considered. Time-dependent solutions to strain energy release rate are obtained by analyzing the balance of the energy. For verification, time-dependent solutions to the strain energy release rate are derived also by considering the time-dependent complementary strain energy. The evolution of the strain energy release rate with the time is analyzed. The effects of material inhomogeneity, locations of the two cracks along the thickness of the arch and the magnitude of the external loading on the time-dependent strain energy release rate are evaluated.

• Journal of the Korean Geotechnical Society
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• v.19 no.3
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• pp.15-22
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• 2003

The appropriate description of the stress-anisotropy and time-dependent behavior of cohesive soils is very important in representing the real soil behavior. In this study, two constitutive relations have been incorporated based on the generalized viscous theory: one is the plastic constitutive relation adopted to capture the stress-anisotropy with a few model parameters; the other is the rate-dependent constitutive relation adopted to describe the strain rate-dependent behavior, an important time-dependent behavior in cohesive soils. The incorporated and proposed constitutive model has relatively a few model parameters and their values need not to be re-evaluated at different strain rates. The proposed model has been verified and investigated with the anisotropic triaxial test results obtained by using the artificial homogeneous specimens.

• Coupled systems mechanics
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• v.11 no.6
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• pp.543-556
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• 2022

Delamination of multilayered inhomogeneous beam that exhibits non-linear relaxation behavior is analyzed in the present paper. The layers are inhomogeneous in the thickness direction. The dealamination crack is located symmetrically with respect to the mid-span. The relaxation is treated by applying a non-linear stress-straintime constitutive relation. The material properties which are involved in the constitutive relation are distributed continuously along the thickness direction of the layer. The delamination is analyzed by applying the J-integral approach. A time-dependent solution to the J-integral that accounts for the non-linear relaxation behavior is derived. The delamination is studied also in terms of the time-dependent strain energy release rate. The balance of the energy is analyzed in order to obtain a non-linear time-dependent solution to the strain energy release rate. The fact that the strain energy release rate is identical with the J-integral value proves the correctness of the non-linear solutions derived in the present paper. The variation of the J-integral value with time due to the non-linear relaxation behavior is evaluated by applying the solution derived.

• Transactions of Materials Processing
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• v.16 no.2 s.92
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• pp.101-106
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• 2007

Uniaxial displacement controlled tests were performed on annealed Type 304 stainless steel at room temperature. A servo-controlled testing machine and strain measurement on the gage length were employed to measure the response to a given input. The test results exhibit that the flow stress increases nonlinearly with the strain rate and the relaxed stress at the end of the relaxation periods depends strongly on the strain rate preceding the relaxation test. The rate-dependent inelastic deformation behavior is simulated using a new unified viscoplasticity model that has the rate-dependent format of nonlinear kinematic hardening rule, which plays a key role in modeling the rate dependence of relaxation behavior. The model does not employ yield or loading/unloading criteria and consists of a flow law and the evolution laws of two tensor and one scalar-valued state variables.

• Steel and Composite Structures
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• v.47 no.3
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• pp.355-363
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• 2023

The main purpose of this study is to characterize the size-dependent strain rate sensitivity in structural steel using the continue stiffness measurement (CSM) indentation. A series of experiments, such as CSM indentation and optical microscope examination, has been performed at the room temperature at different rate conditions. The results indicated that indentation hardness, strain rate, and flow stress showed size-dependent behavior. The dependency of indentation hardness, strain rate, and flow stress on the indentation size was attributed to the transition of the dislocation nucleation rate and the dislocation behaviors during the indentation process. Since both hardness and strain rate showed the size-dependent behavior, SRS tended to depend on the indentation depth. The results indicated that the SRS was quite high over 2.0 at the indentation depth of 240 nm and quickly dropping to 0.08, finally around 0.046 at large indents. The SRS values at large indentations strongly agree with the general range reported for several types of low-carbon steel in the literature (Chatfield and Rote 1974, Nguyen et al. 2018b, Luecke et al. 2005). The results from the present study can be used in both static and dynamic analyses of structures as well as to assess and understand the deformation mechanism and the stress-state of material underneath the indenter tip during the process of the indentation testing.

• Geomechanics and Engineering
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• v.18 no.2
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• pp.133-140
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• 2019

Strain-rate and temperature have significant effects on the one-dimensional (1D) compression behavior of soils. This paper focuses on the bonding degradation effect of soil structure on the time and temperature dependent behavior of soft structured clay. The strain-rate and temperature dependency of preconsolidation pressure are investigated in double logarithm plane and a thermal viscoplastic model considering the combined effect of strain-rate and temperature is developed to describe the mechanical behavior of unstructured clay. By incorporating the bonding degradation, the model is extended that can be suitable for structured clay. The extended model is used to simulate CRS (Constant Rate of Strain) tests conducted on structural Berthierville clay with different strain-rates and temperatures. The comparisons between predicted and experimental results show that the extended model can reasonably describe the effect of bonding degradation on the stain-rate and temperature dependent behavior of soft structural clay under 1D condition. Although the model is proposed for 1D analysis, it can be a good base for developing a more general 3D model.

• Transactions of Materials Processing
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• v.22 no.4
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• pp.216-222
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• 2013

Solid polymers exhibit rate-dependent deformation behavior such as nonlinear strain rate sensitivity and stress relaxation like metallic materials. Despite the different microstructures of polymeric and metallic materials, they have common properties with respect to inelastic deformation. Unlike most metallic materials, solid polymers and shape memory alloys (SMAs) exhibit highly nonlinear stress-strain behavior upon unloading. The present work employs the viscoplasticity theory [K. Ho, 2011, Trans. Mater. Process. 20, 350-356] developed for the pseudoelastic behavior of SMAs, which is based on unified state variable theory for the rate-dependent inelastic deformation behavior of typical metallic materials, to depict the curved unloading behavior of polyphenylene oxide (PPO). The constitutive equations are characterized by the evolution laws of two state variables that are related to the elastic modulus and the back stress. The simulation results are compared with the experimental data obtained by Krempl and Khan [2003, Int. J. Plasticity 19, 1069-1095].

• Transactions of Materials Processing
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• v.17 no.8
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• pp.579-585
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• 2008

Numerous experimental investigations on metallic materials and solid polymers have shown that relaxation behavior is nonlinearly dependent on prior strain rate. The stress drops in a constant time interval nonlinearly increase with an increase of prior strain rate. And the relaxed stress associated with the fastest prior strain rate has the smallest stress magnitude at the end of relaxation periods. This paper deals with the performance of three classes of unified constitutive models in predicting the characteristic behaviors of relaxation. The three classes of models are categorized by a rate sensitivity of kinematic hardening rule. The first class uses rate-independent kinematic hardening rule that includes the competing effect of strain hardening and dynamic recovery. In the second class, a stress rate term is incorporated into the rate-independent kinematic hardening rule. The final one uses a rate-dependent format of kinematic hardening rule.

• Magazine of the Korean Society of Agricultural Engineers
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• v.30 no.4
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• pp.134-153
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• 1988

This paper was carried out to investigate the existence of a unique stress- strain behavior by obtaining some factors influencing the time dependent stress- strain behavior of clay. The results obtained from this study were summarized as follows ; 1. The relationship between stress ratro and strain in normally consolidated clay was in- dependent on pre-shear consolidation pressure. Therefore, shear strain could be expressed as a function with stress ratio. 2. The constitutive equation of shear strain on Modified Carn Clay Model coincided better with the observed value than Cam Clay Model. 3. The relationships between deviator stress and shear strain, between pore water pressure and shear strain were unified by the mean equivalent pressure. 4. The shear strain contour in norrnally consolidated clay was increased linearly through origin, but that in overconsolidated clay was not in accordance with the result of the former. 5. Because the effective stress path of normally consolidated clay was unified by the mean equivalent pressure, state boundary surface in (e,p,q) space was transformed into two dimensional surface. But it was considered to be suitable that the unified stress- strain in overconsolidated clay be expressed by a function with overconsolidation ratio. 6. The deviator for constant strain was increased linearly with increment of strain rate ($\varepsilon$) on semi-log scale, but pore water pressure was decreased. 7. The behavior of stress relaxation was transformed from linear to curvilinear with inc - rement of strain rate before stress relaxation test, and pore water pressure was increased in total range. 8. The strain of creep was increased linearly with increment of time on semi-log scale. The greater the strain rate before creep test became, the greater the increment of strain of creep became. And the pore water pressure during creep test was increased generally with increment of time on semi-log scale.

• Transactions of Materials Processing
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• v.15 no.2 s.83
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• pp.132-137
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• 2006

This paper is concerned with the thermo-mechanical behavior including temperature dependent strain-rate sensitivity of steel sheet for an auto-body. In order to identify the temperature dependent strain-rate sensitivity of SPRC35R and SPRC45E, uniaxial tension tests are performed with the variation of the strain-rates from 0.001 /sec to 200 /sec at environmental temperatures varied from $-40^{\circ}C\;to\;200^{\circ}C$. The thermo-mechanical response at the quasi-static state is obtained with the static tensile test and at the intermediate strain-rate is from the high speed tensile test. Experimental results show that the strain-rate sensitivity increases at low temperature. It represents that as the strain-rate increases, the variation of flow stress becomes sensitive on the temperature. The results indicate that the flow stress of SPRC35R is more dependent on the changes of strain-rate and temperature than those of SPRC45E.