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Penny Shaped Crack Stress Intensity Equation >






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Penny Shaped Crack Stress Intensity Equation

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Consider,,,a,,,plate,,,with,,,dimensions,,,2,,,h,,,,,,2,,,b,,,{displaystyle,,,2htimes,,,2b},,,containing,,,a,,,crack,,,of,,,length,,,2,,,a,,,{displaystyle,,,2a},,,SC.,,,,Paris,,,,PGcriterion[edit]Stress,intensity,factor,and,effective,stiffness,of,a,solid,containing,aligned,penny-shaped,cracksStress,intensity,factors,for,various,modes[edit]

CRC,,PressMode,,I,,,shown,,to,,the,,left,,,is,,an,,opening,,(tensile),,mode,,where,,the,,crack,,surfaces,,move,,directly,,apartHowever,,,if,,the,,crack-tip,,plastic,,zone,,is,,small,,,it,,can,,be,,assumed,,that,,the,,stress,,distribution,,near,,the,,crack,,is,,still,,given,,by,,the,,above,,relationHMSO,,Ministry,,of,,DefenceAlternative,expressions,for,the,stress,intensity,factors,at,A,and,B,are,[7]:175,K,I,A,=,σ,π,a,Φ,A,,,K,I,B,=,σ,π,a,Φ,B,{displaystyle,K{rm,{IA}}=sigma,{sqrt,{pi,a}},Phi,{A},,,K{rm,{IB}}=sigma,{sqrt,{pi,a}},Phi,{B}},where,Φ,A,:=,[,β, ,(,1,−,β,4,),(,1, ,1,4,sec,⁡,α,A,),2,],sec,⁡,α,A,Φ,B,:=,1, ,[,sec,⁡,α,A,B,−,1,1, ,0.21,sin,⁡,{,8,tan,−,1,⁡,[,(,α,A,−,α,B,α,A, ,α,B,),0.9,],},],{displaystyle,{begin{aligned}Phi,{A}&:=left[beta, left({frac,{1-beta,}{4}}right)left(1 {frac,{1}{4{sqrt,{sec,alpha,{A}}}}}right)^{2}right]{sqrt,{sec,alpha,{A}}}Phi,{B}&:=1 left[{frac,{{sqrt,{sec,alpha,{AB}}}-1}{1 0.21sin,left{8,tan,^{-1}left[left({frac,{alpha,{A}-alpha,{B}}{alpha,{A} alpha,{B}}}right)^{0.9}right]right}}}right]end{aligned}}},with,β,:=,sin,⁡,(,π,α,B,α,A, ,α,B,),,,,,,α,A,:=,π,a,2,d,,,,,,α,B,:=,π,a,4,b,−,2,d,,;,,,α,A,B,:=,4,7,α,A, ,3,7,α,B,{displaystyle,,K{rm,,{I}}=sigma,,{sqrt,,{pi,,a}}left[{frac,,{1 3{frac,,{a}{b}}}{2{sqrt,,{pi,,{frac,,{a}{b}}}}left(1-{frac,,{a}{b}}right)^{3/2}}}right],.},,Specimens,,of,,this,,configuration,,are,,commonly,,used,,in,,fracture,,toughness,,testing.[8],,Edge,,crack,,in,,a,,finite,,plate,,under,,uniaxial,,stressσ,,i,,j,,(,,r,,,,,θ,,),,=,,K,,2,,π,,r,,f,,i,,j,,(,,θ,,),, ,,h,,i,,g,,h,,e,,r,,o,,r,,d,,e,,r,,t,,e,,r,,m,,s,,{displaystyle,,sigma,,{ij}(r,theta,,)={frac,,{K}{sqrt,,{2pi,,r}}},f{ij}(theta,,) ,,{rm,,{higher,order,terms}}},,where,,,K,,,{displaystyle,,,K},,,is,,,the,,,stress,,,intensity,,,factor,,,(with,,,units,,,of,,,stress,,,,,,{displaystyle,,,times,,,},,,length1/2),,,and,,,f,,,i,,,j,,,{displaystyle,,,f{ij}},,,is,,,a,,,dimensionless,,,quantity,,,that,,,varies,,,with,,,the,,,load,,,and,,,geometryI.AU,,-,,Sangani,AThe,,stress,,intensity,,factor,,,K,,{displaystyle,,K},,,,,is,,a,,parameter,,that,,amplifies,,the,,magnitude,,of,,the,,applied,,stress,,that,,includes,,the,,geometrical,,parameter,,Y,,{displaystyle,,Y},,(load,,type)

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last edited 29 weeks ago by Chandamo
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