• Advances in materials Research
• /
• 제11권4호
• /
• pp.351-374
• /
• 2022

Softening function is the primary input for modeling the fracture of concrete when the cohesive crack approach is used. In this paper, based on the laboratory data on notched beams, an inverse algorithm is proposed that can accurately find the softening curve of the concrete. This algorithm uses non-linear finite element analysis and the damage-plasticity model. It is based on the kinematics of the beam at the late stages of loading. The softening curve, obtained from the corresponding algorithm, has been compared to other softening curves in the literature. It was observed that in determining the behavior of concrete, the usage of the presented curve made accurate results in predicting the peak loads and the load-deflection curves of the beams with different concrete mixtures. In fact, the proposed algorithm leads to softening curves that can be used for modeling the tensile cracking of concrete precisely. Moreover, the advantage of this algorithm is the low number of iterations for converging to an appropriate answer.

• Computers and Concrete
• /
• 제15권2호
• /
• pp.199-213
• /
• 2015

The residual fracture toughness of post-fire normal-strength concrete subjected up to $600^{\circ}C$ is considered by the wedge splitting test. The initial fracture toughness $K_I^{ini}$ and the critical fracture toughness $K_I^{un}$ could be calculated experimentally. Their difference is donated as the cohesive fracture toughness $K_I^c$ which is caused by the distribution of cohesive stress on the fracture process zone. A comparative study on determining the residual fracture toughness associated with three bi-linear functions of the cohesive stress distribution, i.e. Peterson's softening curve, CEB-FIP Model 1990 softening curve and Xu's softening curve, using an analytical method is presented. It shows that different softening curves have no significant influence on the fracture toughness. Meanwhile, comparisons between the experimental and the analytical calculated critical fracture toughness values further prove the validation of the double-K fracture model to the post-fire concrete specimens.

• Geomechanics and Engineering
• /
• 제8권3호
• /
• pp.323-359
• /
• 2015

This paper presents an elasto-plastic model for determination of the ground response curve of a circular underwater tunnel excavated in elastic-strain softening rock mass compatible with a nonlinear Hoek-Brown yield criterion. The finite difference method (FDM) was used to propose a new solution to calculate pore water pressure, stress, and strain distributions on periphery of circular tunnels in axisymmetric and plain strain conditions. In the proposed solution, a modified non-radial flow pattern, for the hydraulic analysis, is utilized. To evaluate the effect of gravitational loads and variations of pore water pressure, the equations concerning different directions around the tunnel (crown, wall, and floor) are derived. Regarding the strain-softening behavior of the rock mass, the stepwise method is executed for the plastic zone in which parameters of strength, dilatancy, stresses, strains, and deformation are different from their elasto-plastic boundary values as compared to the tunnel boundary values. Besides, the analytical equations are developed for the elastic zone. The accuracy and application of the proposed method is demonstrated by a number of examples. The results present the effects of seepage body forces, gravitational loads and dilatancy angle on ground response curve appropriately.

• Computers and Concrete
• /
• 제5권3호
• /
• pp.261-277
• /
• 2008

This paper presents methodologies for remaining life prediction of plain concrete structural components considering tension softening effect. Non-linear fracture mechanics principles (NLFM) have been used for crack growth analysis and remaining life prediction. Various tension softening models such as linear, bi-linear, tri-linear, exponential and power curve have been presented with appropriate expressions. A methodology to account for tension softening effects in the computation of SIF and remaining life prediction of concrete structural components has been presented. The tension softening effects has been represented by using any one of the models mentioned above. Numerical studies have been conducted on three point bending concrete structural component under constant amplitude loading. Remaining life has been predicted for different loading cases and for various tension softening models. The predicted values have been compared with the corresponding experimental observations. It is observed that the predicted life using bi-linear model and power curve model is in close agreement with the experimental values. Parametric studies on remaining life prediction have also been conducted by using modified bilinear model. A suitable value for constant of modified bilinear model is suggested based on parametric studies.

• 소성∙가공
• /
• 제7권3호
• /
• pp.274-281
• /
• 1998

The service life of tools in metal forming process is to a large extent limited by wear, fatigue fracture and plastic deformation. In elevated temperature forming processes wear is the predominant factor for tool operating life. To predict tool life by wear Achard's model is generally applied. Usually hardness of die is considered to be a function of temperature. But hardness of die is a function of not only tem-perature but also operating time of die. To consider softening of die by repeated operation it is necessary to express hardness of die by a function of a function of temperature and time. By experiment of reheating of die softening curve was obtained and applied to suggest modified Archard's Model in which hardness is a function of main tempering curve.

• International Journal of Concrete Structures and Materials
• /
• 제18권3E호
• /
• pp.191-198
• /
• 2006

The objective of this study is to examine fracture characteristics of concrete at early ages, i.g. critical stress intensity factor, critical crack-tip opening displacement, fracture energy, and bilinear softening curve based on the concepts of effective-elastic crack model and cohesive crack model. A wedge splitting test for Mode I was performed on cubic wedge specimens with a notch at the edge. By experimenting with various strengths and ages, load-crack mouth opening curves were obtained, and the results were analyzed by linear elastic fracture mechanics and FEM(finite element method). The results from the test and analysis showed that critical stress intensity factor and facture energy increased while critical crack-tip opening displacement decreased with concrete aging from 1 day to 28 days. Four parameters of bilinear softening curve from 1 day to 28 days were obtained from a numerical analysis. The obtained fracture parameters and bilinear softening curves at early ages from this study are to be used as a fracture criterion and an input data for the finite element analysis of concrete at early ages.

• 한국콘크리트학회:학술대회논문집
• /
• 한국콘크리트학회 2000년도 봄 학술발표회 논문집
• /
• pp.583-586
• /
• 2000

In this paper, the embedded crack approach that crack is modeled by discontinuous line inside finite element is applied for localized progressive fracture analyses. The algorithm for progressive fracture analyses of concrete structure are enhanced by introducing nonlinear softening curve and unloading algorithm of tension-softening curve which can simulate localized fracture of concrete. The failure analysis results ar compared with existing test results for varification.

• 소성∙가공
• /
• 제10권1호
• /
• pp.35-41
• /
• 2001

The high temperature deformation behavior of SCM 440 can be characterized by the hot torsion test in the temperature ranges of $900^{\circ}C$~$1100^{\circ}C$ and strain rate ranges of 0.05/sec~5/sec. The aim of this paper is to establish the quantitative equation of the volume fraction of dynamic recrystallization (DRX) as a function of processing variables, such as strain rate ($\varepsilon$), temperature (T), and strain ('$\varepsilon$). During hot deformation, the evolution of microstructure could be analyzed from work hardening rate ($\theta$). For the exact prediction of dynamic softening mechanism the critical strain ($\varepsilon_c$), the strain for maximum softening rate ($\varepsilon^*$ and Avrami' exponent (m') were quantitatively expressed by dimensionless parameter, Z/A, respectively. The transformation-effective strain-temperature curve for DRX could be composed. It was found that the calculated results were agreed with the experimental data for the steel at any deformation conditions.

• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 2000년도 추계학술대회 논문집
• /
• pp.33-36
• /
• 2000

The dynamic recrystallization (DRX) of medium carbon steels (SCM 440 and POSMA45) was studied with torsion test in the temperature range of $900-1100^{\circ}C$ and the strain rate range of $5.0x10^{-2}\;-\;5.0x10^0/sec$. To establish the quantitative equations for DRX, the evolution of flow stress curve with strain was analyzed. The critical strain (${\varepsilon}_c$) and strain for maximum softening rate ( ${\varepsilon}^{*}$) could be confirmed by the analysis of work hardening rate ($d{\sigma}/d{\varepsilon}\;=\; \theta$). The volume fraction of dynamic recrystallization ($X_{DRX}$) as a function of processing variables, such as strain rate ( $\dot{\varepsilon}$ ), temperature (T), and strain ( $\varepsilon$ ) were established using the ${\varepsilon}_c$ and ${\varepsilon}^{*}$. For the exact prediction, the ${\varepsilon}_c$, ${\varepsilon}^{*}$ and Avrami' exponent (m') were quantitatively expressed by dimensionless parameter, Z/A respectively. The transformation-effective strain-temperature curve for DRX could be composed. It was found that the calculated results were agreed with the experimental data for the steels at any deformation conditions.

• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 1997년도 춘계학술대회논문집
• /
• pp.77-80
• /
• 1997

The torsion tests in the range of 900~110$0^{\circ}C$, 5.0$\times$10-2~5.0$\times$100/sec were performed to study the recry stallization behavior of 304 stainless steel in the high temperature multistage deformation. The no-recrystallization temperature(Tnr) and fractional softening(FS) were determined by the change of flow curves. The inflection points of stress slope were moved to lower temperature area as the strain rate and the interrupt time were increased. From the multipass flow curve, the intersection between pass stress and FS curve was corresponding to the pass which the FS dropped abruptly and it was shown that the recrystallization area could be determined by the FS measurement in multipass deformation.