混凝土材料V型切口尖端应力—应变场分析
|
摘要
混凝土V型切口问题在实际工程中是经常遇到的,由于在V型切口的尖端存在着应力奇异性,严重地影响了构件的承载能力,很可能成为裂纹的起裂点,因此研究混凝土V型切口尖端的应力-应变场问题具有十分重要的意义。基于此,本文的研究内容如下:
首先,研究了平面应变条件下,混凝土材料的裂纹问题。对压力敏感的混凝土材料,应用弹塑性理论建立了一个新的本构方程,从基本理论出发,结合对裂尖各场合理的奇异性分析,推导出了混凝土材料静态裂纹尖端场的渐进控制方程。
其次,由随V型切口张开角度β变化的不同的定解条件,采用数值分析中的打靶法,对切口尖端场进行了分析。得到应力-应变奇异性随切口张开角度β及幂硬化指数n变化的值。研究了应力-应变场随着切口张开角度β、压力敏感性系数α及幂硬化指数n这三个参数变化的变化规律。
最后,通过将应力场与已知的其它场解进行了比较,论证了本文所得压力敏感性材料的V型切口尖端场的合理性。
本文得到的V型切口尖端场的解为混凝土材料的生产和应用提供了理论参考。
V-notched problems of concrete material are frequently encountered in practical engineering,and they seriously influenced the carrying capacity of the concrete component.As we all know,the tip of the V-notched has singularity,and it is likely to become crack initial point.So researching the stress-strain field problems on the V-notched problems of the concrete material has very important significance.Based on these,the main research items in this dissertation were as follows:
Firstly,the static crack problem in concrete material was detailedly studied under the plane strain condition.A new constitutive equations for pressure-sensitive dilatant materials were also established based on the elastic-plastic theory.At the same time,the asymptotic governing equations were deduced as well with the help of the fundamental equations and the rational analysis on the singularity of crack tip fields.
Secondly,according to the boundary conditions with variational V-notched opening angleβ,the tip field of a V-notched were analyzed by using the shooting method.Stress and strain singularity which were relative to V-notched opening angleβand power hardening index n were also obtained.Meanwhile the changing laws of the stress and strain fields which changed with three coefficients, including V-notched opening angleβ、power hardening index n and pressure sensitivity dilatants coefficientαwere gained as well.
Finally,the tip stress and strain fields on the V-notched of the pressure-sensitive dilatant materials were compared with that in the former document.The results indicated that the conclusions given in this paper were reasonable.
The results here may provide the theoretical references for the production and application of the concrete material.
首先,研究了平面应变条件下,混凝土材料的裂纹问题。对压力敏感的混凝土材料,应用弹塑性理论建立了一个新的本构方程,从基本理论出发,结合对裂尖各场合理的奇异性分析,推导出了混凝土材料静态裂纹尖端场的渐进控制方程。
其次,由随V型切口张开角度β变化的不同的定解条件,采用数值分析中的打靶法,对切口尖端场进行了分析。得到应力-应变奇异性随切口张开角度β及幂硬化指数n变化的值。研究了应力-应变场随着切口张开角度β、压力敏感性系数α及幂硬化指数n这三个参数变化的变化规律。
最后,通过将应力场与已知的其它场解进行了比较,论证了本文所得压力敏感性材料的V型切口尖端场的合理性。
本文得到的V型切口尖端场的解为混凝土材料的生产和应用提供了理论参考。
V-notched problems of concrete material are frequently encountered in practical engineering,and they seriously influenced the carrying capacity of the concrete component.As we all know,the tip of the V-notched has singularity,and it is likely to become crack initial point.So researching the stress-strain field problems on the V-notched problems of the concrete material has very important significance.Based on these,the main research items in this dissertation were as follows:
Firstly,the static crack problem in concrete material was detailedly studied under the plane strain condition.A new constitutive equations for pressure-sensitive dilatant materials were also established based on the elastic-plastic theory.At the same time,the asymptotic governing equations were deduced as well with the help of the fundamental equations and the rational analysis on the singularity of crack tip fields.
Secondly,according to the boundary conditions with variational V-notched opening angleβ,the tip field of a V-notched were analyzed by using the shooting method.Stress and strain singularity which were relative to V-notched opening angleβand power hardening index n were also obtained.Meanwhile the changing laws of the stress and strain fields which changed with three coefficients, including V-notched opening angleβ、power hardening index n and pressure sensitivity dilatants coefficientαwere gained as well.
Finally,the tip stress and strain fields on the V-notched of the pressure-sensitive dilatant materials were compared with that in the former document.The results indicated that the conclusions given in this paper were reasonable.
The results here may provide the theoretical references for the production and application of the concrete material.
引文
[1]Karihaloo B L,Nallathambi P.Effective cracks model for the determination of fracture toughness(K_(Ic)~s) of concrete.Engineering Fracture Mechanics,1990,35(4/5):637-645P
[2]徐世烺,赵国藩.混凝土结构裂纹扩展的KR阻力曲线与双K断裂准则.第五届全国核反应堆结构力学会议文集,成都,1988
[3]Xu S L,Reinhardt H W.Determination of double-K criterion for crack propagation in quasi-brittle fracture,Part Ⅰ:Experimental investigation of crack propagation.International Journal of Fracture,1999,98(2):111-149P
[4]Xu S L,Reinhardt H W.Determination of double-K criterion for crack propagation in quasi-brittle fracture,PartⅡ:Analytical evaluating practical measuring methods for three-point bending notched beams.International Journal of Fracture,1999,98(2):151-177P
[5]Xu S L,Reinhardt H W.Determination of double-K criterion for crack propagation in quasi-brittle fracture,Part Ⅲ:Compact tension specimens and wedge splitting specimens.International Journal of Fracture,1999,98(2):179-193P
[6]Dugdale D S.Yielding of steel containing slit.Journal of the Mechanics and Physics of Solids,1960,8:100-104P
[7]Barenblatt G L.The mathematical theory of equilibrium cracks in brittle fracture.In Advances in Applied Mechanics.Academic Press,1962,7:55-129P
[8]黄向平,王建华.裂纹跟踪的网格生成技术.上海交通大学学报,2001,35(4):493-495页
[9]杨庆生,杨卫.断裂过程的有限元模拟.计算力学学报,1997,14(4):149-154页
[10]Irwin G R.Fracture Dynamics.In:Fracturing of Metals.Cleveland:Am.Soc.Metals,1948:147-166P
[11]Irwin G R.Analysis of stresses and strains near the end of a crack traversing a plate.Journal of Applied Mechanics,1957,24:361-364P
[12]Hutchinson J W.Singular behavior at the end of tensile crack in a hardening material.Journal of Mechanics and Physics of Solids,1968,16(1):13-21P
[13]Rice J R,Rosengren G F.Plane strain deformation near crack tip in a power law hardening material.Journal of Mechanics and Physics of Solids,1968,16(1):1-12P
[14]Li Y C,Wang T C.Higher-order asymptotic field of tension plane strain nonlinear crack problem.Scientia Sinica (Series A),1986,29:941-955P
[15]Hutchinson J W.Plastic stress and strain field at a crack tip.Journal of Mechanics and Physics of Solids,1968,16(4):337-347P
[16]Shih C F.Small-scale yielding analysis of mixed mode plane strain crack problems.Int Fracture analysis.ASTM.STP.,1974,60:187-210P
[17]高玉臣.裂纹起始扩展的弹塑性场.固体力学学报,1980,12(1):67-76页
[18]高玉臣,黄克智.理想弹塑性平面应变问题.力学学报,1981,特刊:111-120页
[19]高玉臣.理想弹塑性平面应力问题.固体力学学报,1982,3(3): 339-350页
[20]Rice J R.A Path Independent Integral and the Approximate Analysis of Strain Concentrations by Notches and Cracks J of Appl.Mech.Vol.,35,NO.2,1968:379-386P
[21]Eshelby J D.Energy relations and the energy-momentum tensor in continuum mechanics.Inelastic Behavior of Solids,1969:77-115P
[22]Cherepanov著,黄克智等译.脆性断裂力学.北京:科学出版社,1990
[23]Bagley J A,Landes J D.The J-integral as a Fracture Criterion.Fracture Toughness.ASTM.STP.,1972,514:1-20P
[24]Hillerborg A,Modeer M,Petersson P E.Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.Cement and Concrete Research,1976,6(6):773-782P
[25]Bazant Z P,Oh B H.Crack band theory for fracture of concrete.RILEM,Materials and structures,1983,16(93):155-177P
[26]Jenq Y S,Shah S P.Two Parameter fracture model for concrete.ASCE,Journal of Engineering Mechanics,1985,111(10):1227-1241P
[27]Bazant Z P,Kazemi M T.Determination of fracture energy,process zone length and brittleness number from size effect,with application to rock and concrete.International Journal of fracture,1990,44:111-131P
[28]徐世娘,赵国藩.混凝土断裂力学研究.大连,大连理工大学出版社,1991
[29]Xu S L,Reinhardt H W.Crack extension resistance and fracture properties of quasi-brittle softening materials like concrete based on the complete process of fracture. International Journal of fracture, 1998, 92(1):71-99P
[30] Reinhardt H W, Xu S L. Crack extension resistance based on the cohesive force in concrete. Engineering Fracture Mechanics, 1999, 64(5):563-557P
[31] Inglis. Stress in a plate due to the presence of cracks and sharp corners. Trans. Inst. Naval Architects, 1913, 55:219-24P
[32] Griffith A A. The phenomena of rupture and flow in solids.phil. Trans. Roy. Soc., of London, 1921, A221:163-197P
[33] M L Williams. Stress singularities resulting from various boundary conditions in angular corners of plates in tension.Journal of Applied Mechanics, 1952, 19:526-528P
[34] Gross B. plane elastic-static analysis of V-notched plate[J].Int J Fracture Mesh, 1972, (8):67-76P
[35] Kuang Z B, Xu X P. Analysis of elastic-plastic sharp notches[J]. Int J Fracture, 1987, (1):39-53P
[36] Atkinson C, Basters J M, Martinezz-Espaola J M. Stress analysis in sharp angular notches using auxiliary fields[J].Engng. Frac Mesh, 1988, (31):637-646P
[37] Yang S, Chao Y J. Asymptotic deformation and stress fields at the tip of a sharp notch in as elastic-plastic material [J].Int J Fracture, 1992, (54):211-224P
[38] Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks [J]. J Appl Mesh, 1968, (35):379-386P
[39]Xia L,Wang T C.Singular near the tip of a sharp Ⅴ-notch in a power law hardening material[J].Int J Fracture,1993,(59):83-93P
[40]Chen D H,Nisitani H.singular stress field near the corner of jointed dissimilar material[J].J Appl Mesh,1993,(60):607-613P
[411 Yakobori T,Kamei A,Konesu S A.Criterion follow-stress brittle fracture of notched specimens based on combined micro and macro fracture with notches[J].Engng Frac Mesh,1976(8):397-409P
[42]Seweryn A.Brittle fracture criterion for structure with sharp notches[J].Engng Frac Mesh,1994,(47):673-681P
[43]郎福元,周爱细,茵执元.非几何对称试件启裂前应力状态的实验研究[J].甘肃工业大学学报,2001,27(4):110-113页
[44]郎福元,周爱细,黄建龙.几何不对称试件启裂前应力变化的激光实验研究[J].甘肃工业大学学报,2001,27(3):107-109页
[45]Li-sha Niu,Hui-Ji Shi,Claude Robin,Guy pluvinage.Elastic and elastce-plastic fields on circular rings containing a Ⅴ-notch under inclined loads[J].Engng Frac Mesh,2001,68:949-962P
[46]Andrzej Seweryn,Andrzej Lukaszewiea.Verification of brittle fracture criteria for elements with Ⅴ-shaped notches.Engng Frac Mesh,2002,69:1487-1510P
[47]Chen D H.Stress intensity factors for Ⅴ-notched strip under tension or in-Plane bending[J].International Journal of Fracture,1995,70:8197P
[48]Lazzarin P,Tovo R.Unified approach to the evaluation of linear elastic stress fields in the neighborhoods of crack and notches. International Journal of Fracture, 1996,78:3-19P
[49] Reddy Jr E D. Asymptotic interface-corner solutions for butt tensile joints. Int.J. Solids Struct,1993,30:767-777P
[50] Aliabadi M H. Boundary element formulation in fracture mechanics. Appl Mech Rev, 1997, 50:83-96P
[51] Liebowitz H, Moyer Jr E T. Finite element methods in fracture mechanics. Comput Sruct,1989, 31:1—9P
[52] Matin L Dun, Wan Suwito, Cunningham S J. Fracture initiation at sharp notches under model I , model Hand mile mixed mode loading. Int. J. Solids Struct,1997, 84:367-381P
[53] Fett T. Failure of brittle materials near stress singularities. Engng Frac Mesh, 1996, 53:511—518P
[54] Reddy Jr E D, Guess T R. Butt tensile joint strength:interface corner stress intensity factor predietion. J Adhesion SciTeeol,1995, 9:237-251P
[55] Andrzej Seweryn. Brittle fracture criterion for structures with sharp notches[J]. Engng Frac Mesh, 1994, 47(5) :673-681P
[56] Suwito W, Dune M L, Cunningham S J. Fracture initiation at sharp notches in single crystal silicon. J. Appl. Phys., 1998,83:3574-3582P
[57] Seweryn A, poskrobko S, Mroz Z. Brittle fracture in plane elements with sharp notches under mixed-mode loading. J Engng Mech ASCE., 1997, 123(6):535-543P
[58] Lazzarin P, Tovo R. A notch intensity factor approach to the stress analysis of welds. Fatigue and Fracture of Engineering Materials and Structure,1998,21:1089-1103P
[59]Chen W F.Plasticity in reinforced concrete.New York:McGraw-Hill,1982P
[60]Chen W F,Mizuno E.Nonlinear analysis in soil mechanics.New York:Elsevier,1990
[61]Harris D.Plasticity models for soil,granular and jointed rock materials.J.Mech.Phys.Solids.,1992,Vol.40(2):273-290P
[62]张学言.岩土塑性力学基础.天津:天津大学出版社,2004
[63]王仁,黄可智,朱兆祥.塑性力学进展.北京:中国铁道出版社,1988
[64]宋建波等.岩体经验强度准则及其在地质工程中的应用.北京:版地质出社,2002
[65]陈惠发.土木工程材料的本构关系.塑性与建模.武汉:华中科技大学出版社,2001
[66]Scha jer G S.Mohr-Coulomb failure criterion expressed in terms of stress invariants.J.of Applied Mechanics,1998,65:1066-1068P
[67]俞茂宏.强度理论百年总结.力学进展,2004,34(4):529-560页
[68]Christensen R M.A comparative evaluation of three isotropic two property failure theories.J.Applied Mechanics,2006,73:852-859P
[69]Christensen R M.A two property yield,failure(fracture)criterion for homogeneous,isotropic materials J.Egn.Mater.Technol.,2004,126:45-52P
[70]Lade P V,Nelson R B,Ito Y M.Instability of Granular materials with non-associated flow.J.Eng.Mech.ASCE.,1988,114:2173-2194P
[71]唐立强,田德谟.一个压力敏感材料的本构方程.哈尔滨船舶工程学院学报,1994,15(1):6-12页
[72]Deshpande V S,Fleck N A.Isotropic constitutive models for metallic foams,Journal of the Mechanics and Physics of Solids,2000,48:1253-1283P
[73]Gioux G,McCormack T M,Gibson L J.Failure of aluminum foams under multiaxial loads,International Journal of Mechanical Sciences,2000,42:1097-1117P
[74]王仁,黄文彬,黄筑平.塑性力学引论.北京:北京大学出版社,1992
[75]王仁,黄可智,朱兆祥.塑性力学进展[M].北京:中国铁道出版社,1988
[76]黄克智,萧纪美主编.材料的损伤断裂机理和宏微观力学理论,北京:清华大学出版社,1999:62-85页
[77]余寿文,冯西桥.损伤力学.北京:清华大学出版社,1997
[78]Lemaitre,Chaboche.固体材料力学.北京:国法工业出版社,1997
[79]Loland K E.Continuos damage model for load-response estimation of concrete.Cement and concrete research,1980,Vol.10:392-492P
[80]Mazars J.A description of micro-and-macro scale damage of concrete structure.Engineering Fracture Mechanics,1986,25(5/6):729-737P
[81]Krajcinovie D,Lemaitre J.Continuum Damage Mechanainstheory and Applications.CISM lecture,Springer-Verlag,1987
[82]李兆霞.损伤力学及其应用.北京:科学出版社,2002
[83]Marakami S,Ohno N.A continuum theory of creep and creep damage.In:ponter A R S,Hayhurst D R,ed.Creep in structures,1981,Berlin:Springer:422-444P
[84]杨卫.宏微观断裂力学.北京:国法工业出版社,1995
[85]Mura T.Micro mechanics of Defects in Solids.Martinis Ni jhoff Publishers,1987
[86]Gurson A L.Continuum theory of ductile rupture in void nucleation and growth part Ⅰ:yiel dcriteria and flow rules for porous ductile media.J Eng Mater Teeh,1977(4):2-15P
[87]MeClintock F A.A criterion for ductile fracture by the growth of holes.J Appl Mech,1968(35):363-371P
[88]Rice J R,Tracey D M.On the ductile enlargement of voids in triaxial stress fields.J M P S,1969(17):201-217P
[89]陈会军.泥岩的本构方程及油水井套管剪切破坏机理的研究.博士论文.哈尔滨:哈尔滨工程大学,2002
[90]Tang L Q,Lou P L.Plane-strain crack-tip asymptotic fields for the concrete materials.Proc.of Int.Sym.on Marine Structure,Shanghai,China,1991:335-338P
[91]陈会军,李永东,唐立强.多孔材料中裂纹尖端的渐进场.哈尔滨工程大学学报,2000,21(3):58-63页
[92]Gross B,Srawley J E,Brown W E.Stress intensity factors for a singular-edge-notch tension specimen by boundary collocation[J].NASA TN D-2395,I964P
[93]Williams M L.On the stress distribution at the base of a stationary crack[J].Jamal of Applied Mechanics,1957,24:109-114P
[2]徐世烺,赵国藩.混凝土结构裂纹扩展的KR阻力曲线与双K断裂准则.第五届全国核反应堆结构力学会议文集,成都,1988
[3]Xu S L,Reinhardt H W.Determination of double-K criterion for crack propagation in quasi-brittle fracture,Part Ⅰ:Experimental investigation of crack propagation.International Journal of Fracture,1999,98(2):111-149P
[4]Xu S L,Reinhardt H W.Determination of double-K criterion for crack propagation in quasi-brittle fracture,PartⅡ:Analytical evaluating practical measuring methods for three-point bending notched beams.International Journal of Fracture,1999,98(2):151-177P
[5]Xu S L,Reinhardt H W.Determination of double-K criterion for crack propagation in quasi-brittle fracture,Part Ⅲ:Compact tension specimens and wedge splitting specimens.International Journal of Fracture,1999,98(2):179-193P
[6]Dugdale D S.Yielding of steel containing slit.Journal of the Mechanics and Physics of Solids,1960,8:100-104P
[7]Barenblatt G L.The mathematical theory of equilibrium cracks in brittle fracture.In Advances in Applied Mechanics.Academic Press,1962,7:55-129P
[8]黄向平,王建华.裂纹跟踪的网格生成技术.上海交通大学学报,2001,35(4):493-495页
[9]杨庆生,杨卫.断裂过程的有限元模拟.计算力学学报,1997,14(4):149-154页
[10]Irwin G R.Fracture Dynamics.In:Fracturing of Metals.Cleveland:Am.Soc.Metals,1948:147-166P
[11]Irwin G R.Analysis of stresses and strains near the end of a crack traversing a plate.Journal of Applied Mechanics,1957,24:361-364P
[12]Hutchinson J W.Singular behavior at the end of tensile crack in a hardening material.Journal of Mechanics and Physics of Solids,1968,16(1):13-21P
[13]Rice J R,Rosengren G F.Plane strain deformation near crack tip in a power law hardening material.Journal of Mechanics and Physics of Solids,1968,16(1):1-12P
[14]Li Y C,Wang T C.Higher-order asymptotic field of tension plane strain nonlinear crack problem.Scientia Sinica (Series A),1986,29:941-955P
[15]Hutchinson J W.Plastic stress and strain field at a crack tip.Journal of Mechanics and Physics of Solids,1968,16(4):337-347P
[16]Shih C F.Small-scale yielding analysis of mixed mode plane strain crack problems.Int Fracture analysis.ASTM.STP.,1974,60:187-210P
[17]高玉臣.裂纹起始扩展的弹塑性场.固体力学学报,1980,12(1):67-76页
[18]高玉臣,黄克智.理想弹塑性平面应变问题.力学学报,1981,特刊:111-120页
[19]高玉臣.理想弹塑性平面应力问题.固体力学学报,1982,3(3): 339-350页
[20]Rice J R.A Path Independent Integral and the Approximate Analysis of Strain Concentrations by Notches and Cracks J of Appl.Mech.Vol.,35,NO.2,1968:379-386P
[21]Eshelby J D.Energy relations and the energy-momentum tensor in continuum mechanics.Inelastic Behavior of Solids,1969:77-115P
[22]Cherepanov著,黄克智等译.脆性断裂力学.北京:科学出版社,1990
[23]Bagley J A,Landes J D.The J-integral as a Fracture Criterion.Fracture Toughness.ASTM.STP.,1972,514:1-20P
[24]Hillerborg A,Modeer M,Petersson P E.Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.Cement and Concrete Research,1976,6(6):773-782P
[25]Bazant Z P,Oh B H.Crack band theory for fracture of concrete.RILEM,Materials and structures,1983,16(93):155-177P
[26]Jenq Y S,Shah S P.Two Parameter fracture model for concrete.ASCE,Journal of Engineering Mechanics,1985,111(10):1227-1241P
[27]Bazant Z P,Kazemi M T.Determination of fracture energy,process zone length and brittleness number from size effect,with application to rock and concrete.International Journal of fracture,1990,44:111-131P
[28]徐世娘,赵国藩.混凝土断裂力学研究.大连,大连理工大学出版社,1991
[29]Xu S L,Reinhardt H W.Crack extension resistance and fracture properties of quasi-brittle softening materials like concrete based on the complete process of fracture. International Journal of fracture, 1998, 92(1):71-99P
[30] Reinhardt H W, Xu S L. Crack extension resistance based on the cohesive force in concrete. Engineering Fracture Mechanics, 1999, 64(5):563-557P
[31] Inglis. Stress in a plate due to the presence of cracks and sharp corners. Trans. Inst. Naval Architects, 1913, 55:219-24P
[32] Griffith A A. The phenomena of rupture and flow in solids.phil. Trans. Roy. Soc., of London, 1921, A221:163-197P
[33] M L Williams. Stress singularities resulting from various boundary conditions in angular corners of plates in tension.Journal of Applied Mechanics, 1952, 19:526-528P
[34] Gross B. plane elastic-static analysis of V-notched plate[J].Int J Fracture Mesh, 1972, (8):67-76P
[35] Kuang Z B, Xu X P. Analysis of elastic-plastic sharp notches[J]. Int J Fracture, 1987, (1):39-53P
[36] Atkinson C, Basters J M, Martinezz-Espaola J M. Stress analysis in sharp angular notches using auxiliary fields[J].Engng. Frac Mesh, 1988, (31):637-646P
[37] Yang S, Chao Y J. Asymptotic deformation and stress fields at the tip of a sharp notch in as elastic-plastic material [J].Int J Fracture, 1992, (54):211-224P
[38] Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks [J]. J Appl Mesh, 1968, (35):379-386P
[39]Xia L,Wang T C.Singular near the tip of a sharp Ⅴ-notch in a power law hardening material[J].Int J Fracture,1993,(59):83-93P
[40]Chen D H,Nisitani H.singular stress field near the corner of jointed dissimilar material[J].J Appl Mesh,1993,(60):607-613P
[411 Yakobori T,Kamei A,Konesu S A.Criterion follow-stress brittle fracture of notched specimens based on combined micro and macro fracture with notches[J].Engng Frac Mesh,1976(8):397-409P
[42]Seweryn A.Brittle fracture criterion for structure with sharp notches[J].Engng Frac Mesh,1994,(47):673-681P
[43]郎福元,周爱细,茵执元.非几何对称试件启裂前应力状态的实验研究[J].甘肃工业大学学报,2001,27(4):110-113页
[44]郎福元,周爱细,黄建龙.几何不对称试件启裂前应力变化的激光实验研究[J].甘肃工业大学学报,2001,27(3):107-109页
[45]Li-sha Niu,Hui-Ji Shi,Claude Robin,Guy pluvinage.Elastic and elastce-plastic fields on circular rings containing a Ⅴ-notch under inclined loads[J].Engng Frac Mesh,2001,68:949-962P
[46]Andrzej Seweryn,Andrzej Lukaszewiea.Verification of brittle fracture criteria for elements with Ⅴ-shaped notches.Engng Frac Mesh,2002,69:1487-1510P
[47]Chen D H.Stress intensity factors for Ⅴ-notched strip under tension or in-Plane bending[J].International Journal of Fracture,1995,70:8197P
[48]Lazzarin P,Tovo R.Unified approach to the evaluation of linear elastic stress fields in the neighborhoods of crack and notches. International Journal of Fracture, 1996,78:3-19P
[49] Reddy Jr E D. Asymptotic interface-corner solutions for butt tensile joints. Int.J. Solids Struct,1993,30:767-777P
[50] Aliabadi M H. Boundary element formulation in fracture mechanics. Appl Mech Rev, 1997, 50:83-96P
[51] Liebowitz H, Moyer Jr E T. Finite element methods in fracture mechanics. Comput Sruct,1989, 31:1—9P
[52] Matin L Dun, Wan Suwito, Cunningham S J. Fracture initiation at sharp notches under model I , model Hand mile mixed mode loading. Int. J. Solids Struct,1997, 84:367-381P
[53] Fett T. Failure of brittle materials near stress singularities. Engng Frac Mesh, 1996, 53:511—518P
[54] Reddy Jr E D, Guess T R. Butt tensile joint strength:interface corner stress intensity factor predietion. J Adhesion SciTeeol,1995, 9:237-251P
[55] Andrzej Seweryn. Brittle fracture criterion for structures with sharp notches[J]. Engng Frac Mesh, 1994, 47(5) :673-681P
[56] Suwito W, Dune M L, Cunningham S J. Fracture initiation at sharp notches in single crystal silicon. J. Appl. Phys., 1998,83:3574-3582P
[57] Seweryn A, poskrobko S, Mroz Z. Brittle fracture in plane elements with sharp notches under mixed-mode loading. J Engng Mech ASCE., 1997, 123(6):535-543P
[58] Lazzarin P, Tovo R. A notch intensity factor approach to the stress analysis of welds. Fatigue and Fracture of Engineering Materials and Structure,1998,21:1089-1103P
[59]Chen W F.Plasticity in reinforced concrete.New York:McGraw-Hill,1982P
[60]Chen W F,Mizuno E.Nonlinear analysis in soil mechanics.New York:Elsevier,1990
[61]Harris D.Plasticity models for soil,granular and jointed rock materials.J.Mech.Phys.Solids.,1992,Vol.40(2):273-290P
[62]张学言.岩土塑性力学基础.天津:天津大学出版社,2004
[63]王仁,黄可智,朱兆祥.塑性力学进展.北京:中国铁道出版社,1988
[64]宋建波等.岩体经验强度准则及其在地质工程中的应用.北京:版地质出社,2002
[65]陈惠发.土木工程材料的本构关系.塑性与建模.武汉:华中科技大学出版社,2001
[66]Scha jer G S.Mohr-Coulomb failure criterion expressed in terms of stress invariants.J.of Applied Mechanics,1998,65:1066-1068P
[67]俞茂宏.强度理论百年总结.力学进展,2004,34(4):529-560页
[68]Christensen R M.A comparative evaluation of three isotropic two property failure theories.J.Applied Mechanics,2006,73:852-859P
[69]Christensen R M.A two property yield,failure(fracture)criterion for homogeneous,isotropic materials J.Egn.Mater.Technol.,2004,126:45-52P
[70]Lade P V,Nelson R B,Ito Y M.Instability of Granular materials with non-associated flow.J.Eng.Mech.ASCE.,1988,114:2173-2194P
[71]唐立强,田德谟.一个压力敏感材料的本构方程.哈尔滨船舶工程学院学报,1994,15(1):6-12页
[72]Deshpande V S,Fleck N A.Isotropic constitutive models for metallic foams,Journal of the Mechanics and Physics of Solids,2000,48:1253-1283P
[73]Gioux G,McCormack T M,Gibson L J.Failure of aluminum foams under multiaxial loads,International Journal of Mechanical Sciences,2000,42:1097-1117P
[74]王仁,黄文彬,黄筑平.塑性力学引论.北京:北京大学出版社,1992
[75]王仁,黄可智,朱兆祥.塑性力学进展[M].北京:中国铁道出版社,1988
[76]黄克智,萧纪美主编.材料的损伤断裂机理和宏微观力学理论,北京:清华大学出版社,1999:62-85页
[77]余寿文,冯西桥.损伤力学.北京:清华大学出版社,1997
[78]Lemaitre,Chaboche.固体材料力学.北京:国法工业出版社,1997
[79]Loland K E.Continuos damage model for load-response estimation of concrete.Cement and concrete research,1980,Vol.10:392-492P
[80]Mazars J.A description of micro-and-macro scale damage of concrete structure.Engineering Fracture Mechanics,1986,25(5/6):729-737P
[81]Krajcinovie D,Lemaitre J.Continuum Damage Mechanainstheory and Applications.CISM lecture,Springer-Verlag,1987
[82]李兆霞.损伤力学及其应用.北京:科学出版社,2002
[83]Marakami S,Ohno N.A continuum theory of creep and creep damage.In:ponter A R S,Hayhurst D R,ed.Creep in structures,1981,Berlin:Springer:422-444P
[84]杨卫.宏微观断裂力学.北京:国法工业出版社,1995
[85]Mura T.Micro mechanics of Defects in Solids.Martinis Ni jhoff Publishers,1987
[86]Gurson A L.Continuum theory of ductile rupture in void nucleation and growth part Ⅰ:yiel dcriteria and flow rules for porous ductile media.J Eng Mater Teeh,1977(4):2-15P
[87]MeClintock F A.A criterion for ductile fracture by the growth of holes.J Appl Mech,1968(35):363-371P
[88]Rice J R,Tracey D M.On the ductile enlargement of voids in triaxial stress fields.J M P S,1969(17):201-217P
[89]陈会军.泥岩的本构方程及油水井套管剪切破坏机理的研究.博士论文.哈尔滨:哈尔滨工程大学,2002
[90]Tang L Q,Lou P L.Plane-strain crack-tip asymptotic fields for the concrete materials.Proc.of Int.Sym.on Marine Structure,Shanghai,China,1991:335-338P
[91]陈会军,李永东,唐立强.多孔材料中裂纹尖端的渐进场.哈尔滨工程大学学报,2000,21(3):58-63页
[92]Gross B,Srawley J E,Brown W E.Stress intensity factors for a singular-edge-notch tension specimen by boundary collocation[J].NASA TN D-2395,I964P
[93]Williams M L.On the stress distribution at the base of a stationary crack[J].Jamal of Applied Mechanics,1957,24:109-114P