A calculation method for the isothermal nucleation incubation time of pro-eutectoid ferrite formed from deformed austenite has been developed by introducing Feder's incubation time expression into the decompositio...A calculation method for the isothermal nucleation incubation time of pro-eutectoid ferrite formed from deformed austenite has been developed by introducing Feder's incubation time expression into the decomposition of deformed austenite.The effects of austenite deformation stored energy and austenite grain boundary energy change on the incubation time have been theoretically calculated and the rule of calculated results is consistent with that of experiments,this confirms that austenite deformation stored energy and the change of austenite grain boundary energy are the natural effect of austenite deformation on ferrite nucleation.展开更多
A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at a large distance from the crack. It was found that ...A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at a large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, the energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values, minimum energy required for initiation of crack growth increases rapidly. The results obtained indicate a possibility to optimise energy consumption of different industrial processes connected with fracture. Much could be gained in, for example, drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e. frequency and amplitude of impacts, for industrial devices, e.g. bores, grinding machines, and hence significantly reduce the process cost. The pre- diction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).展开更多
This paper outlines the results of experimental study of the dynamic rock failure based on the comparison of dry and saturated limestone samples obtained during the dynamic compression and split tests. The tests were ...This paper outlines the results of experimental study of the dynamic rock failure based on the comparison of dry and saturated limestone samples obtained during the dynamic compression and split tests. The tests were performed using the Kolsky method and its modifications for dynamic splitting. The mechanical data(e.g. strength, time and energy characteristics) of this material at high strain rates are obtained. It is shown that these characteristics are sensitive to the strain rate. A unified interpretation of these rate effects, based on the structuraletemporal approach, is hereby presented. It is demonstrated that the temporal dependence of the dynamic compressive and split tensile strengths of dry and saturated limestone samples can be predicted by the incubation time criterion. Previously discovered possibilities to optimize(minimize) the energy input for the failure process is discussed in connection with industrial rock failure processes. It is shown that the optimal energy input value associated with critical load, which is required to initialize failure in the rock media, strongly depends on the incubation time and the impact duration. The optimal load shapes, which minimize the momentum for a single failure impact, are demonstrated. Through this investigation, a possible approach to reduce the specific energy required for rock cutting by means of high-frequency vibrations is also discussed.展开更多
With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precip...With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms~ such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25-x alloy, the incubation time of Llz phases shortens continuously and that of DOzz phases is prolonged. The effects of temperature on the incubation time of Llz and DOzz phases are accordant, i.e. the incuba- tion time is greatly prolonged with the temperature rising.展开更多
On the basis of the classical nucleation theory, a new model of incubation time for austenite to ferrite transformation has been developed, in which the effect of deformation on austenite has been taken into considera...On the basis of the classical nucleation theory, a new model of incubation time for austenite to ferrite transformation has been developed, in which the effect of deformation on austenite has been taken into consideration. To prove the precision of modeling, ferrite transformation starting temperature (Ar3) has been calculated using the Scheil's additivity rule, and the Ar3 values were measured using a Gleeble 1500 thermomechanical simulator. The Ar3 values provided by the modeling method coincide with the measured ones, indicating that the model is precise in oredicting the incubation time for austenite to ferrite transformation in hot deformed steels.展开更多
Nipah (Nypafruticans) is a species of palm trees that grows in mangroves environment near the sea shore. Nipah is potential to produce biofuel energy. The purposes of this research were 1) to determine the optimum ...Nipah (Nypafruticans) is a species of palm trees that grows in mangroves environment near the sea shore. Nipah is potential to produce biofuel energy. The purposes of this research were 1) to determine the optimum bacterial concentration for fermentation to produce high concentration of bio-ethanol, and 2) to determine the optimum incubation time for fermentation to produce high concentration of bio-ethanol. The research had been conducted from June until November 2009 using nipah sap as the substrate and Saceharomyces cerevisiae as a fermentation starter. The experimental design used was a randomized block design (RBD). Factors tested were starter concentration (5%, 7.5%, 10%) and incubation time (2, 4, 6 days). The variables observed were concentration of reducing sugar, total microorganism (CFU/mL), and bio-ethanol production. The results showed that the highest yield of bio-ethanol (8.98%) was produced with 7.5% of starter concentration and 6 days of incubation time.展开更多
Background: The large potential of the soil organic carbon(SOC) pool to sequester CO2from the atmosphere could greatly ameliorate the effect of future climate change. However, the quantity of carbon stored in terrestr...Background: The large potential of the soil organic carbon(SOC) pool to sequester CO2from the atmosphere could greatly ameliorate the effect of future climate change. However, the quantity of carbon stored in terrestrial soils largely depends upon the magnitude of SOC mineralization. SOC mineralization constitutes an important part of the carbon cycle, and is driven by many biophysical variables, such as temperature and moisture.Methods: Soil samples of a pine forest, an oak forest, and a pine and oak mixed forest were incubated for 387 days under conditions with six temperature settings(5 °C, 10 °C, 15 °C, 20 °C, 25 °C, 30 °C) and three levels of soil moisture content(SMC, 30%, 60%, 90%). The instantaneous rate of mineralized SOC was periodically and automatically measured using a Li-Cor CO2analyzer. Based on the measured amount of mineralized SOC,carbon fractions were estimated separately via first-order kinetic one-and two-compartment models.Results: During the 387 day incubation experiment, accumulative mineralized carbon ranged from 22.89 mg carbon(C) ·g-1SOC at 30 °C and 30% SMC for the mixed forest to 109.20 mg C·g-1SOC at 15 °C and 90% SMC for the oak forest. Mineralized recalcitrant carbon varied from 18.48 mg C·g-1SOC at 30 °C and 30% SMC for the mixed forest to 104.98 mg C·g-1SOC at 15 °C and 90% SMC for the oak forest, and contributed at least 80% to total mineralized carbon.Conclusions: Based on the results of this experiment, the soil organic matter of the pure broadleaved forest is more vulnerable to soil microbial degradation in northern China; most of the amount of the mineralized SOC derived from the recalcitrant carbon pool. Labile carbon fraction constitutes on average 0.4% of SOC across the three forest types and was rapidly digested by soil microbes in the early incubation stage. SOC mineralization markedly increased with soil moisture content, and correlated parabolically to temperature with the highest value at 15 °C. No significant interaction was detected among these variables in the present study.展开更多
Jadomycin is an antibiotic that has shown activities against bacteria, yeasts and fungi as well as cytotoxic properties to cancer cells. Because of the wide range of its inhibitory actions, jadomycin shows promise as ...Jadomycin is an antibiotic that has shown activities against bacteria, yeasts and fungi as well as cytotoxic properties to cancer cells. Because of the wide range of its inhibitory actions, jadomycin shows promise as a novel antibiotic and cancer treatment drug. Streptomyces venezuelae are aerobic bacteria that produce jadomycin and the size of bacterial population can significantly affect the yield of jadomycin. Therefore, the bacterial population must be accurately measured in order to standardize the reproducibility of jadomycin production process. In this study, a dehydrogenase activity measurement test, using triphenyl tetrazolium chloride (TTC), was used to measure the dehydrogenase activity of Streptomyces venezuelae during growth in maltose-yeast extract-malt extract (MYM) broth. The aims were to evaluate the effectiveness of the test for measuring microbial growth and to study the effects of the test conditions (incubation time, incubation temperature and medium pH) on triphenyl formazan (TF) yield. The results showed that the TF yield was highly correlated to the optical density. The highest TF yield was observed at a pH of 6 at all incubation times and temperature. Lower TF yields were obtained at higher temperature (40 and 50oC) compared to those obtained at lower temperatures (22 and 30oC). The difference between the yields obtained at 22oC and 30oC were not significant. The differences between incubation time were also not significant. The recommended test conditions are an incubation time of 1 hour at a temperature of 30oC and a pH of 6 followed by three extractions using methanol.展开更多
The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical ques...The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical questions of its numerical implementation are extensively discussed. Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given. The examples include simulations of dynamic crack propagation and arrest, impact crater formation (i.e. fracture in initially intact media), spall fracture in plates, propagation of cracks in pipelines. Applicability of the approach to model initiation, development and arrest of dynamic fracture is claimed.展开更多
We investigated the effects of heating rate on the process parameters of superplastic forming for Zr55Cu30Al10Ni5 by differential scanning calorimetry. The continuous heating and isothermal annealing analyses suggeste...We investigated the effects of heating rate on the process parameters of superplastic forming for Zr55Cu30Al10Ni5 by differential scanning calorimetry. The continuous heating and isothermal annealing analyses suggested that the temperatures of glass transition and onset crystallization are heating rate-dependent in the supercooled liquid region. Then, the time-temperature-transformation diagram under different heating rates indicates that increasing the heating rate can lead to an increase of the incubation time at the same anneal temperature in the supercooled liquid region. Based on the Arrhenius relationship, we discovered that the incubation time increases by 1.08-1.11 times with double increase of the heating rate at the same anneal temperature, and then verified it by the data of literatures and the experimental results. The obtained curve of the max available incubation time reveals that the incubation time at a certain anneal temperature in the supercooled liquid region is not infinite, and will increase with increasing heating rate until this temperature shifts out of the supercooled liquid region because of exceeding critical heating rate. It is concluded that heating rate must be an important processing parameter of superplastic forming for Zr55Cu30Al10Ni5.展开更多
In the present work, we analyse the delamination problem under the combined dynamic load. We show the effect of background harmonic vibrations on critical amplitudes of the principal force pulse. The effect is demonst...In the present work, we analyse the delamination problem under the combined dynamic load. We show the effect of background harmonic vibrations on critical amplitudes of the principal force pulse. The effect is demonstrated on the simple model of a string on an elastic foundation and the fracture phenomenon is predicted by the incubation time criterion. The results state the possibility of considerable decrease in threshold amplitude by a proper choice of the frequency of a background excitation.展开更多
[Objective] This study aimed to investigate the effects of temperature on determination of protein concentration with Coomassie Brilliant Blue method,thus proving advice and guidance for accurate determination of prot...[Objective] This study aimed to investigate the effects of temperature on determination of protein concentration with Coomassie Brilliant Blue method,thus proving advice and guidance for accurate determination of protein concentration.[Method] With Coomassie Brilliant Blue method,the concentrations of different bovine serum albumin samples were determined under different temperatures and incubation time.[Result] According to the standard curve,when the determination range of protein concentration was 0-100 mg/ml,the determined protein concentration was relatively stable after incubation at 20 ℃ for 20-30 min.Furthermore,the determination result of higher protein concentration with Coomassie Brilliant Blue method was less affected by various factors.[Conclusion] In determination of protein concentration with Coomassie Brilliant Blue method,temperature,sample concentration and incubation time were important factors affecting the accuracy of experimental results.展开更多
An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The Creep incompressilility assumption is used Tosimulate fracture behavior of craze region. it is assumed th...An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The Creep incompressilility assumption is used Tosimulate fracture behavior of craze region. it is assumed that in the .fracture processzone near the crack tip, the cohesive stress fo acts upon the crack surfaces and resistscrack opening. Through a perturbation method i. e., by superposing the Mode-Iapplied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelasticproblem is reduced to linear problem. For weak nonlinear materials, for which thepower-law index n=1, the expressions of stress and crack surface displacement arederived. Then, the fracture process zone local energy criterion is proposed and basedon which the formulas of crucking incubation time t. and crack slow propagationvelocity a are derired.展开更多
文摘A calculation method for the isothermal nucleation incubation time of pro-eutectoid ferrite formed from deformed austenite has been developed by introducing Feder's incubation time expression into the decomposition of deformed austenite.The effects of austenite deformation stored energy and austenite grain boundary energy change on the incubation time have been theoretically calculated and the rule of calculated results is consistent with that of experiments,this confirms that austenite deformation stored energy and the change of austenite grain boundary energy are the natural effect of austenite deformation on ferrite nucleation.
文摘A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at a large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, the energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values, minimum energy required for initiation of crack growth increases rapidly. The results obtained indicate a possibility to optimise energy consumption of different industrial processes connected with fracture. Much could be gained in, for example, drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e. frequency and amplitude of impacts, for industrial devices, e.g. bores, grinding machines, and hence significantly reduce the process cost. The pre- diction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).
基金supported by IHC Merwede B.V. as well as by Russian Foundation for Basic Research (Grant Nos. 13-0100349 and 14-01-31510)Russian Science Foundation (“support and development”, Grant No. 14-19-01637)Saint Petersburg University (Grant No. 6.38.243.2014)
文摘This paper outlines the results of experimental study of the dynamic rock failure based on the comparison of dry and saturated limestone samples obtained during the dynamic compression and split tests. The tests were performed using the Kolsky method and its modifications for dynamic splitting. The mechanical data(e.g. strength, time and energy characteristics) of this material at high strain rates are obtained. It is shown that these characteristics are sensitive to the strain rate. A unified interpretation of these rate effects, based on the structuraletemporal approach, is hereby presented. It is demonstrated that the temporal dependence of the dynamic compressive and split tensile strengths of dry and saturated limestone samples can be predicted by the incubation time criterion. Previously discovered possibilities to optimize(minimize) the energy input for the failure process is discussed in connection with industrial rock failure processes. It is shown that the optimal energy input value associated with critical load, which is required to initialize failure in the rock media, strongly depends on the incubation time and the impact duration. The optimal load shapes, which minimize the momentum for a single failure impact, are demonstrated. Through this investigation, a possible approach to reduce the specific energy required for rock cutting by means of high-frequency vibrations is also discussed.
文摘With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms~ such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25-x alloy, the incubation time of Llz phases shortens continuously and that of DOzz phases is prolonged. The effects of temperature on the incubation time of Llz and DOzz phases are accordant, i.e. the incuba- tion time is greatly prolonged with the temperature rising.
文摘On the basis of the classical nucleation theory, a new model of incubation time for austenite to ferrite transformation has been developed, in which the effect of deformation on austenite has been taken into consideration. To prove the precision of modeling, ferrite transformation starting temperature (Ar3) has been calculated using the Scheil's additivity rule, and the Ar3 values were measured using a Gleeble 1500 thermomechanical simulator. The Ar3 values provided by the modeling method coincide with the measured ones, indicating that the model is precise in oredicting the incubation time for austenite to ferrite transformation in hot deformed steels.
文摘Nipah (Nypafruticans) is a species of palm trees that grows in mangroves environment near the sea shore. Nipah is potential to produce biofuel energy. The purposes of this research were 1) to determine the optimum bacterial concentration for fermentation to produce high concentration of bio-ethanol, and 2) to determine the optimum incubation time for fermentation to produce high concentration of bio-ethanol. The research had been conducted from June until November 2009 using nipah sap as the substrate and Saceharomyces cerevisiae as a fermentation starter. The experimental design used was a randomized block design (RBD). Factors tested were starter concentration (5%, 7.5%, 10%) and incubation time (2, 4, 6 days). The variables observed were concentration of reducing sugar, total microorganism (CFU/mL), and bio-ethanol production. The results showed that the highest yield of bio-ethanol (8.98%) was produced with 7.5% of starter concentration and 6 days of incubation time.
基金financially supported by the Fundamental Research Funds for the Central Universities(Grant No.YX2014-10)the Normal Sustainability Fund for the Taiyueshan Long-Term Forest Ecology Research Station(2017-LYPT-DW-148)
文摘Background: The large potential of the soil organic carbon(SOC) pool to sequester CO2from the atmosphere could greatly ameliorate the effect of future climate change. However, the quantity of carbon stored in terrestrial soils largely depends upon the magnitude of SOC mineralization. SOC mineralization constitutes an important part of the carbon cycle, and is driven by many biophysical variables, such as temperature and moisture.Methods: Soil samples of a pine forest, an oak forest, and a pine and oak mixed forest were incubated for 387 days under conditions with six temperature settings(5 °C, 10 °C, 15 °C, 20 °C, 25 °C, 30 °C) and three levels of soil moisture content(SMC, 30%, 60%, 90%). The instantaneous rate of mineralized SOC was periodically and automatically measured using a Li-Cor CO2analyzer. Based on the measured amount of mineralized SOC,carbon fractions were estimated separately via first-order kinetic one-and two-compartment models.Results: During the 387 day incubation experiment, accumulative mineralized carbon ranged from 22.89 mg carbon(C) ·g-1SOC at 30 °C and 30% SMC for the mixed forest to 109.20 mg C·g-1SOC at 15 °C and 90% SMC for the oak forest. Mineralized recalcitrant carbon varied from 18.48 mg C·g-1SOC at 30 °C and 30% SMC for the mixed forest to 104.98 mg C·g-1SOC at 15 °C and 90% SMC for the oak forest, and contributed at least 80% to total mineralized carbon.Conclusions: Based on the results of this experiment, the soil organic matter of the pure broadleaved forest is more vulnerable to soil microbial degradation in northern China; most of the amount of the mineralized SOC derived from the recalcitrant carbon pool. Labile carbon fraction constitutes on average 0.4% of SOC across the three forest types and was rapidly digested by soil microbes in the early incubation stage. SOC mineralization markedly increased with soil moisture content, and correlated parabolically to temperature with the highest value at 15 °C. No significant interaction was detected among these variables in the present study.
文摘Jadomycin is an antibiotic that has shown activities against bacteria, yeasts and fungi as well as cytotoxic properties to cancer cells. Because of the wide range of its inhibitory actions, jadomycin shows promise as a novel antibiotic and cancer treatment drug. Streptomyces venezuelae are aerobic bacteria that produce jadomycin and the size of bacterial population can significantly affect the yield of jadomycin. Therefore, the bacterial population must be accurately measured in order to standardize the reproducibility of jadomycin production process. In this study, a dehydrogenase activity measurement test, using triphenyl tetrazolium chloride (TTC), was used to measure the dehydrogenase activity of Streptomyces venezuelae during growth in maltose-yeast extract-malt extract (MYM) broth. The aims were to evaluate the effectiveness of the test for measuring microbial growth and to study the effects of the test conditions (incubation time, incubation temperature and medium pH) on triphenyl formazan (TF) yield. The results showed that the TF yield was highly correlated to the optical density. The highest TF yield was observed at a pH of 6 at all incubation times and temperature. Lower TF yields were obtained at higher temperature (40 and 50oC) compared to those obtained at lower temperatures (22 and 30oC). The difference between the yields obtained at 22oC and 30oC were not significant. The differences between incubation time were also not significant. The recommended test conditions are an incubation time of 1 hour at a temperature of 30oC and a pH of 6 followed by three extractions using methanol.
基金supported by RFBR research (10-01-00810-a,11-01-00491-a,10-01-91154-GFEN a),Russian Federation State contracts and academic programs of the Russian Academy of Sciences
文摘The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical questions of its numerical implementation are extensively discussed. Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given. The examples include simulations of dynamic crack propagation and arrest, impact crater formation (i.e. fracture in initially intact media), spall fracture in plates, propagation of cracks in pipelines. Applicability of the approach to model initiation, development and arrest of dynamic fracture is claimed.
基金Funded by the National Natural Science Foundation of China(Nos.51175210 and 51175211)
文摘We investigated the effects of heating rate on the process parameters of superplastic forming for Zr55Cu30Al10Ni5 by differential scanning calorimetry. The continuous heating and isothermal annealing analyses suggested that the temperatures of glass transition and onset crystallization are heating rate-dependent in the supercooled liquid region. Then, the time-temperature-transformation diagram under different heating rates indicates that increasing the heating rate can lead to an increase of the incubation time at the same anneal temperature in the supercooled liquid region. Based on the Arrhenius relationship, we discovered that the incubation time increases by 1.08-1.11 times with double increase of the heating rate at the same anneal temperature, and then verified it by the data of literatures and the experimental results. The obtained curve of the max available incubation time reveals that the incubation time at a certain anneal temperature in the supercooled liquid region is not infinite, and will increase with increasing heating rate until this temperature shifts out of the supercooled liquid region because of exceeding critical heating rate. It is concluded that heating rate must be an important processing parameter of superplastic forming for Zr55Cu30Al10Ni5.
基金supported by the Russian Foundation for Basic Research(16-51-53077)the National Natural Science Foundation of China(11611130019)
文摘In the present work, we analyse the delamination problem under the combined dynamic load. We show the effect of background harmonic vibrations on critical amplitudes of the principal force pulse. The effect is demonstrated on the simple model of a string on an elastic foundation and the fracture phenomenon is predicted by the incubation time criterion. The results state the possibility of considerable decrease in threshold amplitude by a proper choice of the frequency of a background excitation.
基金Supported by Natural Science Foundation of Jilin Province(201115221)~~
文摘[Objective] This study aimed to investigate the effects of temperature on determination of protein concentration with Coomassie Brilliant Blue method,thus proving advice and guidance for accurate determination of protein concentration.[Method] With Coomassie Brilliant Blue method,the concentrations of different bovine serum albumin samples were determined under different temperatures and incubation time.[Result] According to the standard curve,when the determination range of protein concentration was 0-100 mg/ml,the determined protein concentration was relatively stable after incubation at 20 ℃ for 20-30 min.Furthermore,the determination result of higher protein concentration with Coomassie Brilliant Blue method was less affected by various factors.[Conclusion] In determination of protein concentration with Coomassie Brilliant Blue method,temperature,sample concentration and incubation time were important factors affecting the accuracy of experimental results.
文摘An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The Creep incompressilility assumption is used Tosimulate fracture behavior of craze region. it is assumed that in the .fracture processzone near the crack tip, the cohesive stress fo acts upon the crack surfaces and resistscrack opening. Through a perturbation method i. e., by superposing the Mode-Iapplied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelasticproblem is reduced to linear problem. For weak nonlinear materials, for which thepower-law index n=1, the expressions of stress and crack surface displacement arederived. Then, the fracture process zone local energy criterion is proposed and basedon which the formulas of crucking incubation time t. and crack slow propagationvelocity a are derired.