Failurecriteria& Failure modes

1 Failure criteria & Failure modes1 Strength of orthotropic laminaThe strength is defined by 5 quantitiesThtthitliththdi tiThe strengthvaries stronglywiththe directionThe Failure analysis is always donein the (L,T) frame21. Maximum stress theoryThe Failure occurs if one of the stresses in the naturalaxes (L,T) exceeds the corresponding allowable avoid Failure , the material must satisfy the followingIlitiInequalities:In compression:Assumes that the Failure modes are independent !3 Example: Glass epoxy composite With the normalized properties: Lscale !! ogarithmicL LTLo TT42. Maximum strain theoryyThe Failure occurs if one of the strainsin the naturalaxes (L,T) exceeds the corresponding avoidfailure, the materialmust satisfythe followingInequalities:In compressionIf the material is elasticlinear until Failure , 5 Comparison Maximum stress theory Maximum strain theoryMaximum stress criterionMaximum strain criterionIn stress space6 Expressing the maximum strain criterion in stress space:7 Maximum stresscriterionMaximum strain theory:The Failure occurs if one of the following inequalities holds:PoissoneffectPoisson effect>>L>LTThe maximum stress theoryand the maximum strain theoryyIgnore the interaction betweenthe Failure Hill criterion8 StressdeviatortensorTsai Hill criterion, preliminary.

2 Von Mises criterionStress deviatortensorobtained by subtracting the hydrostatic stress from the stress tensorThe stress deviator has the same principaldirections as the stress tensor. The invariantsJ1, J2and J3of the stress deviator are defined byBecauseJ1=0, the stress deviator tensorisinastateofpureshearisin a state of pure shear9 BecauseJ1=0, the stress deviator tensor is in a state of pure Mises criterion1,pvon Mises had the intuition thatthe yielding of materialsbeginswhenthe second deviatoric stress invariant J2reaches a critical value. It is straightforward to determine the critical value from a uniaxial tension test:In principal axes:The criterion is also called the criterion of Maximum distortion strain energy(Hencky) OctahedralshearstressOctahedralshearstre ss10 Maximum distortion strain energy(Hencky) InprincipalaxesStress strain relationshipIn principal axes:Hydrostatic stress state: uniform stress:Proportional to J211 Yielding occurs when:In plane stresses: 12 For orthotropic materials, the criterion needs to be expressed in the material axes (L,T)von Mises in an arbitrary (non principal) frame:Extended to anisotropic behaviour by Hill (1948).

3 By analogy, Tsai Hill assumethat Failure occurs if the inequality is violated:PlanestressesPlane stresses:Finally:Consistent with T!!!13 LTsai Hill: example of glass epoxy compositeTBoth Land Tare in traction Accountsfortheinteractionbetweenthefailu remodesTsai HillAccountsfor the interaction betweenthe failuremodes Conservative The maximum difference occurs at the change of Failure modes One must transform the stress state in the (L,T) frame14von Mises in principal plane stresses:Tsai Hill in plane stresses (L,T)15 Importance of the sign of shear stress on the strength of composites16 Glass epoxyStep 1:Transform in(L,T) frame:Step 2:Tsai Hillcriterion17 Ultimate strength xy= 5 MPa xy= Mpa18 Failure modes Breaking of the fiberskfh Microcracking of the matrix Debonding(separation of the interface between matrix and fibers) Delamination(separation of laminae from each other)19 Microcracking in glass reinforced epoxy201.

4 Failure under longitudinale tensile loadIndividual fibers break in a random mannerat less than 50% of the ultimate load. DependingonthetypeoffibersandmatrixandVD ependingon the type of fibersand matrixand VfThe following Failure modes are observed: Brittle fracture. Brittle with fiber pullout (matrix breaking away from the fibers). Shear Failure of the matrix and fibers: Vf< <Vf< Vf> Failure under longitudinale compression loadFailure modes : Transverse tensile Failure Fiber microbuckling (extension mode or shear mode) Shear failureShear failureVfsmall Vflarge23 Microbuckling in shear mode (large Vf)Extension mode(low Vf)24 Based on the assumption of transverse tensile Failure of the matrix,and on the empirical formula ( ) (composite transverse breaking strain):one can develop a model for the longitudinal compressive stress:AtfailureAtfailure:Rule of mixtures:Dominated by 25ythe matrix !

5 3. Failure under transverse tensile loadsFailure modes :Fibers perpendicular to the loading produce stress concentrationsattheinterfaceandinthematr ixconcentrations atthe interface and in the Failure occurs because of the matrix or the interface tensile Failure (occasionally highly orientedfibers may also break in the transverse direction)26274. Failure under transverse compression loadsFailure modes : Matrix shear Failure Matrix shear Failure plus debonding285. Failure under in plane shear loadsFailure modes :Mihfil Matrixshearfailure Constituent debonding29