ENB331 Materials and Manufacturing 2 Week 5.docx

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Queensland University of Technology
Prasad Yarlagadda

ENB331 Lecture Materials and Manufacturing 2 Griffith Critical Stress A balance between surface energy and strain energy E = Modulus of elasticity γs= Specific surface energy a = Half the internal crack length Fracture Toughness (K ) IC KICs a measure of a materials resistance to brittle fracture when a crack is present KIC Material selection σ = Design stress a = Allowable flaw size or NDT flaw detection Stress Distribution around crack tip in a thin infinite plate Generalized Hooke’s Law A uniaxial stress gives rise to a triaxial state of strain Total strains (Generalized Hooke’s Law) 1 Week 5 Tuesday, 27 August 2013 ENB331 Lecture Materials and Manufacturing 2 Effect of material thickness on local stresses and strains If a plate is very thin, only local stresses σ and σ (biaxial In thicker sections, crack root is constrained by material x y tension) are induced. No localized tensile stress along on either side and thus the strain along z-axis is zero (ε =z the z-axis (σz= 0) and is called Plane Stress as one of the 0). This is called Plain Strain as one of the principal principal stresses is zero. From equation 6, the local strains is zero. From equation 6: stresses cause a negative strain at the crack root. Negative strain means thinning of the plate (free contraction) near the crack tip due to the high value of σ x and σ y The constrained material induced stress σ and zhis creates triaxial tension. Effect of material thickness on fracture toughness Fracture toughness depends on volume of a material and thus the thickness. Thinner materials exhibit higher toughness (due to only biaxial tension) and this is known as plane stress fracture toughness. Thicker materials have lower limit of material toughness (due to triaxial tension) and is known as plane strain fracture toughness Plastic Zone Elastic Stress Equations: As r goes to 0 (at crack tip), local stresses σx,ynd to infinity and such high stress magnitudes do not occur in structures. Irwin argued that once local stresses starts to exceed the yield stress of the material, plastic deformation occurs at the crack tip and thus stress singularity cannot exist. Approximations were done to determine the amount of plastic deformation at the crack tip using plastic zone. Irwin assumed circular shape of the plastic zone. Only situation along x-axis (θ=0) for σ will be ynalysed. Plastic Zone, ry 2 Week 5 Tuesday, 27 August 2013 ENB331 Lecture Materials and Manufacturing 2 Fracture Mode Transition Full plane stress occurs if the calculated size of the plastic zone is approximately the same as the thickness of the specimen, B. Predominant plane strain is expected when the calculated plastic zone size is approximately 1/10 of the thickness. Plane strain fracture toughness (KIC remained constant with thickness and thus shows material property. Strength vs Fracture toughness Yield strength – Stress level that produces permanent plastic deformation Fracture strength – stress level that causes failure Fracture toughness – stress-intensity level at the crack tip that causes failure. Typically as materials get stronger, the fracture toughness decreases. How to improve both toughness and strength Microstructure refinement (grain size reduction) improves toughness and strength. Smaller grains:  Smaller dislocation pile-ups at grain boundaries  Less chance for cracks to form Grain growth in steel is retarded by addition of vanadium, titanium, niobium, aluminium and to a lesser extent by nickel. Vanadium (as little as 0.1% is the most potent grain-refining element by forming finely dispersed carbides and nitrides in steel. Fracture Toughness Measurements The most common Fracture Toughness test configurations are: Compact tension, Single Edge Notch Bend (SENB) and Notched Round. W = width of specimen B = thickness of specimen D = diameter for round specimen The position and orientation of
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