Steady Load Failure Theories

Transcription

1 tea Loa Failure Theories Ductile Materials Uniaxial tress/train Fiel Maximum-Normal-tress Maximum-Normal-train Maximum-hear-tress Distortion-Energ hear-energ Von Mises-Henck Octaheral-hear-tress Internal-Friction Fracture Mechanics Brittle Materials Multiaxial tress/train Fiel Man theories have been put forth some agree reasonabl well with test ata, some o not.

2 The Maximum-Normal Normal-tress Theor Postulate: Failure occurs when one of the three principal stresses equals the strength.,, an are principal stresses > > Failure occurs when either Tension t t c trength in Tension trength in Compression c Compression

3 Maximum-Normal Normal-tress Failure urface (Biaxial Conition) locus of failure states t - c t Accoring to the Maximum-Normal-tress Theor, as long as stress state falls within the box, the material will not fail. - c

4 ~ Maximum-Normal Normal-tress Failure urface (Three-imensional Case) ~ ~ t Accoring to the Maximum-Normal-tress Theor, as long as stress state falls within the box, the material will not fail. - c

5 The Maximum-Normal Normal-train Theor (aint-venant s Theor) Postulate: Yieling occurs when the largest of the three principal strains becomes equal to the strain corresponing to the iel strength. Eε Eε Eε ν ν ν ( + ) ( + ) ± ( ) + ± ± E Young's Moulus ν Poisson's Ratio

6 Maximum-Normal Normal-train Theor (Biaxial Conition) locus of failure states ν ν ± ± - - As long as the stress state falls within the polgon, the material will not iel.

7 Maximum-hear hear-tress tress Theor (Tresca Criterion) Postulate: Yieling begins whenever the maximum shear stress in a part becomes equal to the maximum shear stress in a tension test specimen that begins to iel. / max > > / /, tress tate in Part Tensile Test pecimen

8 Maximum-hear hear-tress tress Theor (Continue) Tensile Test pecimen s 0.5 The shear iel strength is equal to one-half of the tension iel strength. max s,

9 Maximum-hear hear-tress tress Theor (Continue) / / / max > > tress tate in Part / / / max

10 Maximum-hear hear-tress tress Theor (Continue) s From Mohr s circle for a tensile test specimen / max From Mohr s circle for a threeimensional stress state.

11 Maximum Maximum-hear hear-tress Theor tress Theor (Hrostatic Effect) (Hrostatic Effect) ( ) h h h h I Principal stresses will alwas have a hrostatic component (equal pressure) / / / The maximum shear stresses are inepenent of the hrostatic stress. > eviatoric component h > hrostatic

12 Maximum-hear hear-tress tress Theor (Hrostatic Effect Continue) Hrostatic tress tate If Then max 0, an there is no ieling regarless of the magintue of the hrostatic stress. The Maximum-hear-tress Theor postulates that ieling is inepenent of a hrostatic stress.

13 Maximum-hear hear-tress tress Theor (Biaxial Representation of the Yiel urface) Yieling will occur if an of the following criteria are met. For biaxial case (plane stress) 0 ± ± ± ± ± ± In general, all three conitions must be checke.

14 Maximum-hear hear-tress tress Theor (Biaxial Representation of the Yiel urface) For biaxial case (plane stress) 0 ± ± ± - II III - locus of failure states I IV Note that in the I an III quarants the Maximum-hear- tress Theor an Maximum-Normal-tress Theor are the same for the biaxial case.

15 Maximum-hear hear-tress tress Theor (Three-imensional Representation of the Yiel urface) failure surface Hamrock, Fig. 6.9

16 Assignment Failure Theories, Rea ection 5-9. (a) Fin the bening an transverse shear stress at points A an B in the figure. (b) Fin the maximum normal stress an maximum shear stress at both points. (c) For a iel point of 50,000 psi, fin the factor of safet base on the maximum normal stress theor an the maximum shear stress theor.