Fracture Mechanics - Materials Technology

1 Fracture MechanicsLecture notes - course 4A780 Concept SchreursEindhoven University of TechnologyDepartment of Mechanical EngineeringMaterials TechnologySeptember 6, 2012 Contents1 Introduction12 Fracture Fracture mechanisms .. Shearing .. Cleavage .. Fatigue .. Crazing .. De-adhesion .. Ductile - brittle behavior .. Charpy v-notch test .. Theoretical strength .. Discrepancy with experimental observations .. Griffith s experiments .. Crack loading modes .. 183 Experimental Surface cracks.

2 Electrical resistance .. X-ray .. Ultrasound .. Acoustic emission .. Adhesion tests ..214 Fracture Energy balance .. Griffith s energy balance .. Griffith stress .. Discrepancy with experimental observations .. Compliance change .. Fixed grips .. Constant load .. Experiment .. Examples .. 29 III5 Stress Deformation and strain .. Stress .. Linear elastic material behavior .. Equilibrium equations .. Plane stress .. Plane strain .. Displacement method.

3 Stress function method .. Circular hole in infinite plate .. Elliptical hole .. 446 Crack tip Complex plane .. Complex variables .. Complex functions .. Laplace operator .. Bi-harmonic equation .. Solution of bi-harmonic equation .. Stresses .. Displacement .. Choice of complex functions .. Displacement components .. Mode I .. Displacement .. Stress components .. Stress intensity factor .. Crack tip solution .. Mode II .. Displacement.

4 Stress intensity factor .. Crack tip solution .. Mode III .. Laplace equation .. Displacement .. Stress components .. Stress intensity factor .. Crack tip solution .. Crack tip stress (mode I, II, III) .. SIF for specified cases .. crack growth criteria .. RelationG K.. The critical SIF value .. 62 III7 Multi-mode crack Stress component transformation .. Multi-mode load .. Crack growth direction .. Maximum tangential stress criterion .. Strain energy density (SED) criterion.

5 728 Dynamic Fracture Crack growth rate .. Elastic wave speeds .. Crack tip stress .. Crack branching .. Fast Fracture and crack arrest .. Experiments ..829 Plastic crack tip Von Mises and Tresca yield criteria .. Principal stresses at the crack tip .. Von Mises plastic zone .. Tresca plastic zone .. Influence of the plate thickness .. Shear planes .. Plastic zone in the crack plane .. Irwin plastic zone correction .. Dugdale-Barenblatt plastic zone correction.

6 Plastic constraint factor .. Plastic zones in the crack plane .. Small Scale Yielding .. 9210 Nonlinear Fracture Crack-tip opening displacement .. CTOD by Irwin .. CTOD by Dugdale .. CTOD crack growth criterion .. Integral along closed curve .. Path independence .. RelationJ K.. HRR crack tip stresses and strains .. Ramberg-Osgood material law .. HRR-solution .. crack growth criterion .. 10111 Numerical Fracture Quadratic elements .. Crack tip mesh .. Special elements.

7 Quarter point elements .. One-dimensional case .. Virtual crack extension method (VCEM) .. Stress intensity factor .. J-integral .. Domain integration .. De LorenziJ-integral : VCE technique .. Crack growth simulation .. Node release .. Moving Crack Tip Mesh .. Element splitting .. Smeared crack approach .. 11412 Crack surface .. Experiments .. Fatigue load .. Fatigue limit .. (S-N)-curve .. Influence of average stress .. (P-S-N)-curve .. High/low cycle fatigue .. Basquin relation.

8 Manson-Coffin relation .. Total strain-life curve .. Influence factors .. Load spectrum .. Stress concentrations .. Stress gradients .. Material properties .. Surface quality .. Environment .. Crack growth .. Crack growth models .. Paris law .. Fatigue life .. Other crack grow laws .. Crack growth at low cycle fatigue .. Load spectrum .. Random load .. Tensile overload .. Design against fatigue .. 13713 Engineering plastics (polymers) Mechanical properties .. Damage .. Properties of engineering plastics.

9 Fatigue .. 141A Laplace equationa1B Derivatives of Airy functiona3 Chapter 1 IntroductionImportant aspects of technological and biological structures are stiffness and strength. Re-quirements on stiffness, being the resistance against reversible deformation, may vary over awide range. Strength, the resistance against irreversibledeformation, is always required tobe high, because this deformation may lead to loss of functionality and even global :Stiffness and mechanicsWhen material properties and associated mechanical variables can be assumed to be con-tinuous functions of spatial coordinates, analysis of mechanical behavior can be done withContinuum Mechanics .

10 This may also apply to permanent deformation, although this is as-sociated with structural changes, phase transformation, dislocation movement, molecularslip and breaking of atomic bonds. The only requirement is that the material behavior isstudied on a scale, large enough to allow small scale discontinuities to be averaged a three-dimensional continuum is subjected to external loads it will deform. Thestrain components, which are derived from the displacementsui(i= 1,2,3) by differentiation ( ),j with respect to spatial coordinatesxj(j= 1,2,3), are related by the stress components ij(i,j= 1,2,3) must satisfy the equilibrium equations partialdifferential equations and boundary most cases the equilibrium equations are impossible to solve without taking intoaccount the material behavior, which is characterized by a material model, relating stresscomponents ijto strain components kl(k,l= 1,2,3).