1MaterialPropertiesGeol341-342J. Toro2004Many diagrams are from Earth Structure, van der Pluijm and Marshak, 2004Outline• Modes of deformation– Ductile vs. Brittle behavior• Stress-Strain Relationships– Elasticity– Viscosity– Plasticity• Role of– Temperature– Pressure– Strain RateCauses and Consequences• Differential Stress – Cause of deformation• Strain – The consequence of differential Stress• Quantitative relationship?• Example: Mohr-Coulomb failureMechanical Behavior depends on Material Properties• Solid?• Liquid?• Plastic?•…2What is a Solid? What is a Liquid?Solid• Strong•Hard• Maintains shape•Deforms proportionally to loadLiquid•Weak•Soft (?)• Takes shape of vessel• Deforms under any loadWhat about Play-Do ?• Shares some properties with both solids and liquids• Plastic materialElastic Solids• Example 1: Ruler• Example 2: Rock and HammerStress-Strain Relationship• “Ut tensio sic uis” (Robert Hooke,1676)• “Extension is proportional to the applied force”•F = K ∆ x3Linear Elastic BehaviorF = K ∆ x−σ = Ε . estressYoung’s ModulusExtension (strain)Young’s Modulus• Elastic constant• Like the spring constant• Units of Stress• Plexiglass E= 3 Gpa• Shale E= 10-30 Gpa• Granite E= 40-70 Gpa• Basalt E= 60-80 Gpa• Steel E= 200 GpaCalculating Elastic Strain (1 D)• Example:σn= 100 MPa (lithostatic stress at 3.8 km depth)E= 10 GPa = 10,000 MPae= -σn/Ee= -100 /10,000e= -0.01 = -1%plotWhat happens when you pull on a rubber band?•It gets longer …. And skinnier!•Poisson’s Ratio υ = | −exx/eyy|υ = 0.5 incompressible material (no volume loss) Rocks υ = 0.1 to 0.3examples4Stress-Strain in 3D• We need to consider the contribution of the perpendicular stressesexx= - (1/E) (σxx - υ (σyy + σzz))Strain along x Young’s modulusPoisson ratioStresssesFluids• Viscous behavior• Non-recoverable deformation• Continue to deform regardless of how small the stress• Resistance is proportional to strain rate• Strain is time-dependentFluidsStrain Rateσ = 2 ηêViscosity coef.5How do rocks behave?• Mixed behavior• Non-linear• Elastic at low strain• Plastic at high strainLimestone Deformation Variable Confining PressureElasticPlasticYield PointDeformation Experiments Effect of Confining Pressure6Effect of TemperatureSolnhofen LimestoneEffect of Strain RateYule MarbleFastSlowCrustal Strength