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Paul C Paris - One of the best experts on this subject based on the ideXlab platform.
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about the effect of Plastic Dissipation in heat at the crack tip on the stress intensity factor under cyclic loading
International Journal of Fatigue, 2014Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palinluc, Nicolas SaintierAbstract:Abstract Because of the reverse cyclic Plastic zone at the crack tip, there is Plastic Dissipation in heat at the crack tip under cyclic loading. That creates a heterogeneous temperature field around the crack tip. A thermo-mechanical model is proposed in this paper for evaluating the consequence of this temperature field on the Mode I stress intensity factor. Two cases are studied: (i) the theoretical problem of an infinite plate with a semi-infinite through crack under Mode I cyclic loading, and (ii) a finite specimen with a central through crack. In the first case, the main hypothesis and results are presented from the literature but no heat loss is taken into account. In second case, heat loss by convection is taken into account with a finite element analysis, while an analytical solution exists in the literature for the first case. In both cases, it is assumed that the heat source is located in the reverse cyclic Plastic zone. The heat source within the reverse cyclic Plastic zone is quantified by experiments on a mild steel under R = 0.1. It is shown that the crack tip is under compression due to thermal stresses coming from the heterogeneous temperature field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum, minimum and its range) is calculated. This paper shows that experiments have to be carried out to determine the heat source within the reverse cyclic Plastic zone. This is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor.
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On the effect of fatigue crack Plastic Dissipation on the stress intensity factor
2013Co-Authors: Nicolas Ranc, Thierry Palin-luc, Paul C ParisAbstract:In metals, during Plastic strain, a significant part of the Plastic energy is converted into heat. This generates a heterogeneous temperature field around the crack tip which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure under cyclic loading. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to stress field around the crack tip. This paper shows how this thermal effect modifies the mode one stress intensity factor for two cases: (i) the theoretical problem of an infinite plate with a semi-infinite through crack and (ii) a finite plate specimen with a central through crack. The comparison of the two cases allows the authors to discuss the effect of convection. The comparison of the simulated and experimental temperature field variation at the specimen surface (infra-red measurement on a mild steel) leads to identify the heat flux in the reverse cyclic Plastic zone. This is the key parameter of the problem. Finally, the consequences of the calculation on the range, the ratio and the maximum and the minimum values of the stress intensity factor are discussed.
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003 under cyclic loading Plastic Dissipation in heat at the crack tip modifies the stress intensity factor
Principles and Practice of Constraint Programming, 2013Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palinluc, Nicolas SaintieAbstract:Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic Plastic zone. The analytical solution of the thermomechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated for the infinite plate. The heat flux within the reverse cyclic Plastic zone is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor. INTRODUCTION During a cyclic loading of a crack, the Plasticity is located in the reverse cyclic Plastic zone near the crack tip which was first explained by Paris in 1964 [1] and studied later by Rice in 1967 [2]. This effect is now well known and participates for instance in the explanation of the crack closure phenomenon which was noted by Elber in 1970 [3]. In metals, during Plastic strain, a significant part of the Plastic energy (around 90% [4, 5]) is converted into heat. The dissipated energy in the reverse cyclic Plastic zone also generates an heterogeneous temperature field which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to stress field in this region. The objective of this work is to quantify the effect on the stress intensity factor of this heterogeneous temperature field. However, there are two significant problems in order to estimate the thermal stresses: the first is the quantification of the heat source associated with the Plasticity near the crack tip and the second is to make a good estimation of the boundary conditions of the thermal problem (convection from the
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The effect on the mode I stress intensity factor of Plastic Dissipation in heat at the crack tip under cyclic loading.
2013Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palin-luc, Nicolas SaintierAbstract:Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for two problems: (i) an infinite plate with a semi-infinite through crack and (ii) a centre cracked plate specimen, both under mode I cyclic loading. The heat source is assumed to be located in the reverse cyclic Plastic zone (RCPZ). The solution of the thermomechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous temperature field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated. The heat flux within the RCPZ is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor. Introduction During a cyclic loading of a crack, the cyclic Plasticity is located in the reverse cyclic Plastic zone (RCPZ) near the crack tip which was first explained by Paris in 1964 [1] and studied later by Rice in 1967 [2]. The effect of crack closure during cyclic loading [3] must also be considered. In metals, during Plastic strain, a significant part of the Plastic energy (around 90% [4, 5]) is converted into heat. The dissipated energy in the RCPZ also generates a heterogeneous temperature field which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure [6]. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to the stress field in this region. The objective of this work is to quantify the effect on the stress intensity factor of these heterogeneous temperature and stress induced fields for a crack under cyclic loading in mode I. The proposed paper presents first the main results of Ranc et al. [6] about the theoretical problem of an infinite plate with a semi-infinite through crack loaded in fatigue in mode I where thermal losses due to convection and radiation are neglected. Then experimental data are presented and analysed with a FEA model which consider convective thermal losses. Finally, the consequences of the calculation on the range, the ratio and the maximum and the minimum values of the stress intensity factor are discussed. Some recommendations for further theoretical and experimental investigations are proposed. General Considerations about Dissipation in Heat at the crack Tip under Cyclic Loading During fatigue crack growth under cyclic loading, the cyclic Plastic strains at each cycle are confined within the RCPZ. A proportion of the Plastic strain energy is dissipated in heat and generates a temperature variation. Generally, the size of this RCPZ is very small compared to the crack length and the cracked structure dimensions. To determine the temperature field due to Dissipation in heat at the crack tip, Ranc et al. [6] have shown that the hypothesis of a line heat source located within the RCPZ is correct. The temperature variation field obtained with the line heat source and the uniform heat source hypothesis within the RCPZ are very close together outside the RCPZ. Note that the computation of the temperature field within the RCPZ is not needed in this study. The dissipated power per unit length of crack front is assumed to be proportional to the surface area of the RCPZ and the loading frequency f [7] 2 R r fη = fξ = q , with ξ the dissipated energy per unit length of crack front during one cycle, R r the radius of the RCPZ and η a material dependent proportionality factor. Since in plane stress or in plain strain the RCPZ radius is proportional to 2 I ΔK , where I ΔK is the range of variation of the mode I stress intensity factor, it is clear that the dissipated power per unit length of crack front is therefore proportional to the variation of the stress intensity factor to the power four. These results have been already shown analytically [7] and numerically [8]. A constant heat source will be considered in this paper. Furthermore, note that in general the fatigue crack velocity is small, especially when the stress intensity range ΔK is close to the threshold value th ΔK . Since q is proportional to 4 ΔK , for a slow moving crack, ΔK and the heat source q can be assumed constant. Moreover, in such case the heat source associated with the fatigue crack propagation can also be considered to be motionless [6]. The Case of an Infinite Plate with a Semi-Infinite Through Crack The temperature variation field. For an infinite plate with a semi-infinite through crack under mode one cyclic loading with all the previous assumptions, the thermal problem is axisymetric and if the line heat source is along the z axis which is the normal direction to the surface of the plate, the associated heat transfer equation is (1) where is the density of the material, C its heat capacity, its heat conductivity and (r) the Dirac function.
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thermal effect of Plastic Dissipation at the crack tip on the stress intensity factor under cyclic loading
Engineering Fracture Mechanics, 2011Co-Authors: Nicolas Ranc, Thierry Palinluc, Paul C ParisAbstract:Abstract Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic Plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic Plastic zone is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor.
Nicolas Ranc - One of the best experts on this subject based on the ideXlab platform.
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about the effect of Plastic Dissipation in heat at the crack tip on the stress intensity factor under cyclic loading
International Journal of Fatigue, 2014Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palinluc, Nicolas SaintierAbstract:Abstract Because of the reverse cyclic Plastic zone at the crack tip, there is Plastic Dissipation in heat at the crack tip under cyclic loading. That creates a heterogeneous temperature field around the crack tip. A thermo-mechanical model is proposed in this paper for evaluating the consequence of this temperature field on the Mode I stress intensity factor. Two cases are studied: (i) the theoretical problem of an infinite plate with a semi-infinite through crack under Mode I cyclic loading, and (ii) a finite specimen with a central through crack. In the first case, the main hypothesis and results are presented from the literature but no heat loss is taken into account. In second case, heat loss by convection is taken into account with a finite element analysis, while an analytical solution exists in the literature for the first case. In both cases, it is assumed that the heat source is located in the reverse cyclic Plastic zone. The heat source within the reverse cyclic Plastic zone is quantified by experiments on a mild steel under R = 0.1. It is shown that the crack tip is under compression due to thermal stresses coming from the heterogeneous temperature field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum, minimum and its range) is calculated. This paper shows that experiments have to be carried out to determine the heat source within the reverse cyclic Plastic zone. This is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor.
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On the effect of fatigue crack Plastic Dissipation on the stress intensity factor
2013Co-Authors: Nicolas Ranc, Thierry Palin-luc, Paul C ParisAbstract:In metals, during Plastic strain, a significant part of the Plastic energy is converted into heat. This generates a heterogeneous temperature field around the crack tip which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure under cyclic loading. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to stress field around the crack tip. This paper shows how this thermal effect modifies the mode one stress intensity factor for two cases: (i) the theoretical problem of an infinite plate with a semi-infinite through crack and (ii) a finite plate specimen with a central through crack. The comparison of the two cases allows the authors to discuss the effect of convection. The comparison of the simulated and experimental temperature field variation at the specimen surface (infra-red measurement on a mild steel) leads to identify the heat flux in the reverse cyclic Plastic zone. This is the key parameter of the problem. Finally, the consequences of the calculation on the range, the ratio and the maximum and the minimum values of the stress intensity factor are discussed.
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003 under cyclic loading Plastic Dissipation in heat at the crack tip modifies the stress intensity factor
Principles and Practice of Constraint Programming, 2013Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palinluc, Nicolas SaintieAbstract:Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic Plastic zone. The analytical solution of the thermomechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated for the infinite plate. The heat flux within the reverse cyclic Plastic zone is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor. INTRODUCTION During a cyclic loading of a crack, the Plasticity is located in the reverse cyclic Plastic zone near the crack tip which was first explained by Paris in 1964 [1] and studied later by Rice in 1967 [2]. This effect is now well known and participates for instance in the explanation of the crack closure phenomenon which was noted by Elber in 1970 [3]. In metals, during Plastic strain, a significant part of the Plastic energy (around 90% [4, 5]) is converted into heat. The dissipated energy in the reverse cyclic Plastic zone also generates an heterogeneous temperature field which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to stress field in this region. The objective of this work is to quantify the effect on the stress intensity factor of this heterogeneous temperature field. However, there are two significant problems in order to estimate the thermal stresses: the first is the quantification of the heat source associated with the Plasticity near the crack tip and the second is to make a good estimation of the boundary conditions of the thermal problem (convection from the
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The effect on the mode I stress intensity factor of Plastic Dissipation in heat at the crack tip under cyclic loading.
2013Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palin-luc, Nicolas SaintierAbstract:Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for two problems: (i) an infinite plate with a semi-infinite through crack and (ii) a centre cracked plate specimen, both under mode I cyclic loading. The heat source is assumed to be located in the reverse cyclic Plastic zone (RCPZ). The solution of the thermomechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous temperature field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated. The heat flux within the RCPZ is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor. Introduction During a cyclic loading of a crack, the cyclic Plasticity is located in the reverse cyclic Plastic zone (RCPZ) near the crack tip which was first explained by Paris in 1964 [1] and studied later by Rice in 1967 [2]. The effect of crack closure during cyclic loading [3] must also be considered. In metals, during Plastic strain, a significant part of the Plastic energy (around 90% [4, 5]) is converted into heat. The dissipated energy in the RCPZ also generates a heterogeneous temperature field which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure [6]. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to the stress field in this region. The objective of this work is to quantify the effect on the stress intensity factor of these heterogeneous temperature and stress induced fields for a crack under cyclic loading in mode I. The proposed paper presents first the main results of Ranc et al. [6] about the theoretical problem of an infinite plate with a semi-infinite through crack loaded in fatigue in mode I where thermal losses due to convection and radiation are neglected. Then experimental data are presented and analysed with a FEA model which consider convective thermal losses. Finally, the consequences of the calculation on the range, the ratio and the maximum and the minimum values of the stress intensity factor are discussed. Some recommendations for further theoretical and experimental investigations are proposed. General Considerations about Dissipation in Heat at the crack Tip under Cyclic Loading During fatigue crack growth under cyclic loading, the cyclic Plastic strains at each cycle are confined within the RCPZ. A proportion of the Plastic strain energy is dissipated in heat and generates a temperature variation. Generally, the size of this RCPZ is very small compared to the crack length and the cracked structure dimensions. To determine the temperature field due to Dissipation in heat at the crack tip, Ranc et al. [6] have shown that the hypothesis of a line heat source located within the RCPZ is correct. The temperature variation field obtained with the line heat source and the uniform heat source hypothesis within the RCPZ are very close together outside the RCPZ. Note that the computation of the temperature field within the RCPZ is not needed in this study. The dissipated power per unit length of crack front is assumed to be proportional to the surface area of the RCPZ and the loading frequency f [7] 2 R r fη = fξ = q , with ξ the dissipated energy per unit length of crack front during one cycle, R r the radius of the RCPZ and η a material dependent proportionality factor. Since in plane stress or in plain strain the RCPZ radius is proportional to 2 I ΔK , where I ΔK is the range of variation of the mode I stress intensity factor, it is clear that the dissipated power per unit length of crack front is therefore proportional to the variation of the stress intensity factor to the power four. These results have been already shown analytically [7] and numerically [8]. A constant heat source will be considered in this paper. Furthermore, note that in general the fatigue crack velocity is small, especially when the stress intensity range ΔK is close to the threshold value th ΔK . Since q is proportional to 4 ΔK , for a slow moving crack, ΔK and the heat source q can be assumed constant. Moreover, in such case the heat source associated with the fatigue crack propagation can also be considered to be motionless [6]. The Case of an Infinite Plate with a Semi-Infinite Through Crack The temperature variation field. For an infinite plate with a semi-infinite through crack under mode one cyclic loading with all the previous assumptions, the thermal problem is axisymetric and if the line heat source is along the z axis which is the normal direction to the surface of the plate, the associated heat transfer equation is (1) where is the density of the material, C its heat capacity, its heat conductivity and (r) the Dirac function.
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thermal effect of Plastic Dissipation at the crack tip on the stress intensity factor under cyclic loading
Engineering Fracture Mechanics, 2011Co-Authors: Nicolas Ranc, Thierry Palinluc, Paul C ParisAbstract:Abstract Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic Plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic Plastic zone is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor.
Nicolas Saintier - One of the best experts on this subject based on the ideXlab platform.
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about the effect of Plastic Dissipation in heat at the crack tip on the stress intensity factor under cyclic loading
International Journal of Fatigue, 2014Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palinluc, Nicolas SaintierAbstract:Abstract Because of the reverse cyclic Plastic zone at the crack tip, there is Plastic Dissipation in heat at the crack tip under cyclic loading. That creates a heterogeneous temperature field around the crack tip. A thermo-mechanical model is proposed in this paper for evaluating the consequence of this temperature field on the Mode I stress intensity factor. Two cases are studied: (i) the theoretical problem of an infinite plate with a semi-infinite through crack under Mode I cyclic loading, and (ii) a finite specimen with a central through crack. In the first case, the main hypothesis and results are presented from the literature but no heat loss is taken into account. In second case, heat loss by convection is taken into account with a finite element analysis, while an analytical solution exists in the literature for the first case. In both cases, it is assumed that the heat source is located in the reverse cyclic Plastic zone. The heat source within the reverse cyclic Plastic zone is quantified by experiments on a mild steel under R = 0.1. It is shown that the crack tip is under compression due to thermal stresses coming from the heterogeneous temperature field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum, minimum and its range) is calculated. This paper shows that experiments have to be carried out to determine the heat source within the reverse cyclic Plastic zone. This is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor.
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The effect on the mode I stress intensity factor of Plastic Dissipation in heat at the crack tip under cyclic loading.
2013Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palin-luc, Nicolas SaintierAbstract:Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for two problems: (i) an infinite plate with a semi-infinite through crack and (ii) a centre cracked plate specimen, both under mode I cyclic loading. The heat source is assumed to be located in the reverse cyclic Plastic zone (RCPZ). The solution of the thermomechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous temperature field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated. The heat flux within the RCPZ is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor. Introduction During a cyclic loading of a crack, the cyclic Plasticity is located in the reverse cyclic Plastic zone (RCPZ) near the crack tip which was first explained by Paris in 1964 [1] and studied later by Rice in 1967 [2]. The effect of crack closure during cyclic loading [3] must also be considered. In metals, during Plastic strain, a significant part of the Plastic energy (around 90% [4, 5]) is converted into heat. The dissipated energy in the RCPZ also generates a heterogeneous temperature field which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure [6]. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to the stress field in this region. The objective of this work is to quantify the effect on the stress intensity factor of these heterogeneous temperature and stress induced fields for a crack under cyclic loading in mode I. The proposed paper presents first the main results of Ranc et al. [6] about the theoretical problem of an infinite plate with a semi-infinite through crack loaded in fatigue in mode I where thermal losses due to convection and radiation are neglected. Then experimental data are presented and analysed with a FEA model which consider convective thermal losses. Finally, the consequences of the calculation on the range, the ratio and the maximum and the minimum values of the stress intensity factor are discussed. Some recommendations for further theoretical and experimental investigations are proposed. General Considerations about Dissipation in Heat at the crack Tip under Cyclic Loading During fatigue crack growth under cyclic loading, the cyclic Plastic strains at each cycle are confined within the RCPZ. A proportion of the Plastic strain energy is dissipated in heat and generates a temperature variation. Generally, the size of this RCPZ is very small compared to the crack length and the cracked structure dimensions. To determine the temperature field due to Dissipation in heat at the crack tip, Ranc et al. [6] have shown that the hypothesis of a line heat source located within the RCPZ is correct. The temperature variation field obtained with the line heat source and the uniform heat source hypothesis within the RCPZ are very close together outside the RCPZ. Note that the computation of the temperature field within the RCPZ is not needed in this study. The dissipated power per unit length of crack front is assumed to be proportional to the surface area of the RCPZ and the loading frequency f [7] 2 R r fη = fξ = q , with ξ the dissipated energy per unit length of crack front during one cycle, R r the radius of the RCPZ and η a material dependent proportionality factor. Since in plane stress or in plain strain the RCPZ radius is proportional to 2 I ΔK , where I ΔK is the range of variation of the mode I stress intensity factor, it is clear that the dissipated power per unit length of crack front is therefore proportional to the variation of the stress intensity factor to the power four. These results have been already shown analytically [7] and numerically [8]. A constant heat source will be considered in this paper. Furthermore, note that in general the fatigue crack velocity is small, especially when the stress intensity range ΔK is close to the threshold value th ΔK . Since q is proportional to 4 ΔK , for a slow moving crack, ΔK and the heat source q can be assumed constant. Moreover, in such case the heat source associated with the fatigue crack propagation can also be considered to be motionless [6]. The Case of an Infinite Plate with a Semi-Infinite Through Crack The temperature variation field. For an infinite plate with a semi-infinite through crack under mode one cyclic loading with all the previous assumptions, the thermal problem is axisymetric and if the line heat source is along the z axis which is the normal direction to the surface of the plate, the associated heat transfer equation is (1) where is the density of the material, C its heat capacity, its heat conductivity and (r) the Dirac function.
Nicolas Saintie - One of the best experts on this subject based on the ideXlab platform.
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003 under cyclic loading Plastic Dissipation in heat at the crack tip modifies the stress intensity factor
Principles and Practice of Constraint Programming, 2013Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palinluc, Nicolas SaintieAbstract:Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic Plastic zone. The analytical solution of the thermomechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated for the infinite plate. The heat flux within the reverse cyclic Plastic zone is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor. INTRODUCTION During a cyclic loading of a crack, the Plasticity is located in the reverse cyclic Plastic zone near the crack tip which was first explained by Paris in 1964 [1] and studied later by Rice in 1967 [2]. This effect is now well known and participates for instance in the explanation of the crack closure phenomenon which was noted by Elber in 1970 [3]. In metals, during Plastic strain, a significant part of the Plastic energy (around 90% [4, 5]) is converted into heat. The dissipated energy in the reverse cyclic Plastic zone also generates an heterogeneous temperature field which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to stress field in this region. The objective of this work is to quantify the effect on the stress intensity factor of this heterogeneous temperature field. However, there are two significant problems in order to estimate the thermal stresses: the first is the quantification of the heat source associated with the Plasticity near the crack tip and the second is to make a good estimation of the boundary conditions of the thermal problem (convection from the
Thierry Palinluc - One of the best experts on this subject based on the ideXlab platform.
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about the effect of Plastic Dissipation in heat at the crack tip on the stress intensity factor under cyclic loading
International Journal of Fatigue, 2014Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palinluc, Nicolas SaintierAbstract:Abstract Because of the reverse cyclic Plastic zone at the crack tip, there is Plastic Dissipation in heat at the crack tip under cyclic loading. That creates a heterogeneous temperature field around the crack tip. A thermo-mechanical model is proposed in this paper for evaluating the consequence of this temperature field on the Mode I stress intensity factor. Two cases are studied: (i) the theoretical problem of an infinite plate with a semi-infinite through crack under Mode I cyclic loading, and (ii) a finite specimen with a central through crack. In the first case, the main hypothesis and results are presented from the literature but no heat loss is taken into account. In second case, heat loss by convection is taken into account with a finite element analysis, while an analytical solution exists in the literature for the first case. In both cases, it is assumed that the heat source is located in the reverse cyclic Plastic zone. The heat source within the reverse cyclic Plastic zone is quantified by experiments on a mild steel under R = 0.1. It is shown that the crack tip is under compression due to thermal stresses coming from the heterogeneous temperature field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum, minimum and its range) is calculated. This paper shows that experiments have to be carried out to determine the heat source within the reverse cyclic Plastic zone. This is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor.
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003 under cyclic loading Plastic Dissipation in heat at the crack tip modifies the stress intensity factor
Principles and Practice of Constraint Programming, 2013Co-Authors: Nicolas Ranc, Paul C Paris, Thierry Palinluc, Nicolas SaintieAbstract:Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic Plastic zone. The analytical solution of the thermomechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated for the infinite plate. The heat flux within the reverse cyclic Plastic zone is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor. INTRODUCTION During a cyclic loading of a crack, the Plasticity is located in the reverse cyclic Plastic zone near the crack tip which was first explained by Paris in 1964 [1] and studied later by Rice in 1967 [2]. This effect is now well known and participates for instance in the explanation of the crack closure phenomenon which was noted by Elber in 1970 [3]. In metals, during Plastic strain, a significant part of the Plastic energy (around 90% [4, 5]) is converted into heat. The dissipated energy in the reverse cyclic Plastic zone also generates an heterogeneous temperature field which depends on the intensity of the heat source associated with the Plasticity and the thermal boundary conditions of the cracked structure. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to stress field in this region. The objective of this work is to quantify the effect on the stress intensity factor of this heterogeneous temperature field. However, there are two significant problems in order to estimate the thermal stresses: the first is the quantification of the heat source associated with the Plasticity near the crack tip and the second is to make a good estimation of the boundary conditions of the thermal problem (convection from the
-
thermal effect of Plastic Dissipation at the crack tip on the stress intensity factor under cyclic loading
Engineering Fracture Mechanics, 2011Co-Authors: Nicolas Ranc, Thierry Palinluc, Paul C ParisAbstract:Abstract Plastic Dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic Plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic Plastic zone is the key parameter to quantify the effect of Dissipation at the crack tip on the stress intensity factor.