形状不連続部付平板の非貫通型欠陥に対する曲げ疲労寿命予測 (第1報):疲労き裂の形状変化とその表現式について Part-Through Crack Bending Fatigue Life Prediction of a Plate with Geometrical Discontinuity (Part I):Formulation of Part Through Fatigue Crack Shape

Bending fatigue tests were performed using plates with transverse (grooves, fillets and protuberances) and through-thickness geometrical discontinuity (holes and grooves) in addition to plain plates. Shape change in fatigue crack growing from surface and corner flaws was investigated and the equation for expression of crack shape was proposed. The conclusions are summarized as follows : <BR>(1) Shape change in part-through fatigue crack growing in a plate with geometrical discontinuity was classified into equilibrated and non-equilibrated growth in the same way as shape change in fatigue surface crack growing in plain plate.<BR>(2) The equation for expression of the fatigue crack shape for the equilibrated growth was induced by simplification of the stress-field where fatigue crack grew ; for plain plate, <BR><I>b</I>/<I>a</I>=1-<I>b</I>/<I>t</I>, <BR>for transverse geometrical discontinuity plate, <BR><I>b</I>/<I>a</I>=1- (<I>b</I>/<I>t</I>) <SUP>1/<I>K<SUB>t</SUB></I></SUP>, <BR>and, for through-thickness geometrical discontinuity plate, <BR><I>b</I>/<I>a</I>= 1/ {∑<I>k</I> <I>i</I>=1 <I>C<SUB>i</SUB></I> (1+<I>a</I>/ρ) <SUP>-2 (<I>i</I>-1) </SUP>+ (2-1/<I>K<SUB>t</SUB></I>) <I>a</I>/<I>t</I>} (<I>b</I>/<I>t</I><0.5) 1/<I>K<SUB>t</SUB></I>/ {∑<I>k</I> <I>i</I>=1 <I>C<SUB>i</SUB></I> (1+<I>a</I>/ρ) <SUP>-2 (<I>i</I>-1) </SUP>+1/<I>K<SUB>t</SUB></I>·<I>a</I>/<I>t</I>} (<I>b</I>/<I>t</I>≥0.5) <BR>(3) The equation for expression of the fatigue crack shape for the non-equilibrated growth was induced by considering the relation between the initial flaw shape and the equilibrated growth crack shape ;<BR>for plain plate, <BR><I>b</I>/<I>a</I>= <I>b</I>/<I>t</I>/ {(<I>b</I>/<I>t</I>/1-<I>b</I>/<I>t</I>) <SUP><I>m</I></SUP>+ (<I>a</I>*/<I>t</I>) <SUP><I>m</I></SUP>} <SUP>1/<I>m</I></SUP> (<I>a<SUB>0</SUB></I>>><I>b<SUB>0</SUB></I>) 1/ {1- (<I>b</I>*/<I>t</I>/<I>b</I>/<I>t</I>) <SUP><I>n</I></SUP>} <SUP>1/<I>n</I></SUP> (<I>a<SUB>0</SUB></I><<<I>b<SUB>0</SUB></I>) <BR>for transverse geometrical discontinuity plate, <BR><I>b</I>/<I>a</I>= <I>b</I>/<I>t</I>/ [{(<I>b</I>/<I>t</I>/1-<I>b</I>/<I>t</I>) <SUP>1/<I>K<SUB>t</SUB></I></SUP>} + (<I>a</I>*/<I>t</I>) <SUP><I>m</I></SUP>] <SUP>1/<I>m</I></SUP>(<I>a<SUB>0</SUB></I>>><I>b<SUB>0</SUB></I>) 1/ {1- (<I>b</I>*/<I>t</I>/<I>b</I>/<I>t</I>) <SUP><I>n</I></SUP>} <SUP>1/<I>n</I></SUP>- (<I>b</I>/<I>t</I>) <SUP>1/<I>K<SUB>t</SUB></I></SUP> (<I>a<SUB>0</SUB></I><<<I>b<SUB>0</SUB></I>) <BR>and, for through-thickness geometrical discontinuity plate, <BR><I>b</I>/<I>a</I>= 1/ {∑<I>k</I> <I>i</I>=1 <I>C<SUB>i</SUB></I> (1+<I>a</I>/ρ) <SUP>-2 (<I>i</I>-1) </SUP>/ {1- (<I>a</I>*/<I>t</I>/<I>a</I>/<I>t</I>) <SUP><I>m</I></SUP>} <SUP>1/<I>m</I></SUP>+ (2-1/<I>K<SUB>t</SUB></I>) <I>a</I>/<I>t</I> (<I>b</I>/<I>t</I><0.5) 1/<I>K<SUB>t</SUB></I>/ ∑<I>k</I> <I>i</I>=1 <I>C<SUB>i</SUB></I> (1+<I>a</I>/ρ) <SUP>-2 (<I>i</I>-1) </SUP>/ {1- (<I>a</I>*/<I>t</I>/<I>a</I>/<I>t</I>) <SUP><I>m</I></SUP>} <SUP>1/<I>m</I></SUP>+1/<I>K<SUB>t</SUB></I>·<I>a</I>/<I>t</I>} (<I>b</I>/<I>t</I>≥0.5) (<I>a<SUB>0</SUB></I>>><I>b<SUB>0</SUB></I>) <BR>and<BR><I>b</I>/<I>a</I>= [1/ {∑<I>k</I> <I>i</I>=1 <I>C<SUB>i</SUB></I> (1+<I>a</I>/ρ) <SUP>-2 (<I>i</I>-1) </SUP>+ (2-1/<I>K<SUB>t</SUB></I>) <I>a</I>/<I>t</I>} <SUP><I>n</I></SUP>+ (<I>b</I>*/<I>t</I>/<I>a</I>/<I>t</I>) <SUP><I>n</I></SUP>] <SUP>1/<I>n</I></SUP> (<I>b</I>/<I>t</I><0.5) [1/<I>K<SUP>n</SUP><SUB>t</SUB></I>/ {∑<I>k</I> <I>i</I>=1 <I>C<SUB>i</SUB></I> (1+<I>a</I>/ρ) <SUP>-2 (<I>i</I>-1) </SUP>+1/<I>K<SUB>t</SUB></I>·<I>a</I>/<I>t</I>} <SUP><I>n</I></SUP>+ (<I>b</I>*/<I>t</I>/<I>a</I>/<I>t</I>) <SUP><I>n</I></SUP>] <SUP>1/<I>n</I></SUP> (<I>b</I>/<I>t</I>≥0.5) (<I>a<SUB>0</SUB></I><<<I>b<SUB>0</SUB></I>)