MatE 22 Module 4.2 - Deformations of Crystalline Materials PDF

MatE 22 Structure-Property Relationship of Materials II Plastic Deformation MODULE 4.2 Lecture slides adapted from previous MatE 22 classes (Ma’am Tiff Lao) Learning Outcomes Identify the different types of deformation Differentiate slipping and twinning plastic deformation...

MatE 22 Structure-Property Relationship of Materials II Plastic Deformation MODULE 4.2 Lecture slides adapted from previous MatE 22 classes (Ma’am Tiff Lao) Learning Outcomes Identify the different types of deformation Differentiate slipping and twinning plastic deformation MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Deformation change in dimension or shape of a material brought about by Learning Outcomes an applied stress Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Have two (2) types Elastic Types of Twinning Plastic Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Elastic Strain (atomic perspective) elastic region tensile (temporary deformation) no breaking of bonds compression The magnitude of elastic strains depends on the interatomic bonding forces. stronger interatomic bonds, higher Higher? Lower? __ elastic modulus, Higher? Lower? __ resistance to elastic deformation higher MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez Plastic deformation can be… plastic region (permanent Reasons: (not limited to the ff: ) deformation) Unwarranted deformation Miscalculated mechanical properties Catastrophic events Non-maintenance of the material Reasons: (not limited to the ff: ) hot or cold-working Warranted deformation Alter the mechanical properties of the material, i.e., hardening/non-hardening MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Plastic Strain (atomic perspective) plastic region (permanent deformation) The magnitude of plastic strains depends on the imperfection of a material. defects Types of defects 1. Point 2. Line dislocations 3. Surface a linear or one-dimensional defect around which some of the atoms are misaligned MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Plastic Strain (atomic perspective) plastic region (permanent deformation) The magnitude of plastic strains depends on the imperfection of a material. defects Types of defects 1. Point 2. Line 3. Surface Twin defect a surface defect which crystals on either side of a plane are mirror images of each other Brennecka90deg%20bend%20Thumb Plasticity of materials is explained using Dislocation Theory. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Theoretical and Actual Yield Learning Outcomes Strengths of Metals Plastic Deformation Theoretical YS Measured YS Slipping (MPa) (MPa) Edge, Screw, Mixed Aluminum 11,000 26 Stress Field Nickel 32,000 234 Slip along Atomic Planes Silver 13,000 131 Resolved Shear Stress Mild Steel 34,000 207 Slipping of Single vs Polycrystalline Titanium 19,000 172 Twinning Twin Plane Types of Twinning Due to the advent of electron microscopes, dislocations were Slipping vs Twinning readily observed, and dislocation theory was developed further. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why do metals deform easily? Learning Outcomes Why is actual yield strength lower than the theoretical? Plastic Deformation Slipping Edge, Screw, Mixed This is due to the presence of DISLOCATIONS! Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Dislocation Motion Slip Learning Outcomes Process of plastic deformation by dislocation motion Plastic Deformation Slip Plane Slipping crystallographic plane where dislocation traverses Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline slip plane Twinning slip Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip difficult in a perfect Learning Outcomes lattice? Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Because one must break bond SIMULTANEOUSLY Types of Twinning before lattice movement happens Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes dislocation line Plastic Deformation Slipping Edge, Screw, Mixed shear stress Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning shear stress Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes dislocation line Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes dislocation line Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes dislocation line Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Why is slip easy in defective lattice? Learning Outcomes dislocation line Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Burger’s Vector Slipping of Single vs Polycrystalline magnitude and direction of the Twinning lattice distortion resulting from a Twin Plane dislocation in a crystal lattice Types of Twinning Slipping vs Twinning Because the atoms must break bonds ONE AT A TIME ONLY! MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  How does deformation occur? Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez Learning Outcomes If dislocations don't move, slip deformation doesn't happen! Plastic Deformation Slipping Edge, Screw, Mixed From this point on, the general assumption is that we are Stress Field considering a defective lattice since perfect crystals are not Slip along Atomic Planes naturally made. Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip There are three (3) types of dislocation motion/slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress slip plane Slipping of Single vs Polycrystalline Twinning Parallel or Dislocation line Burger’s vector Slip plane Twin Plane Perpendicular? Types of Twinning Edge Dislocation Slipping vs Twinning dislocation ⊥ || || motion MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Learning Outcomes There are three (3) types of dislocation motion/slip: Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge slip plane Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Burger’s Vector Resolved Shear Stress Slipping of Single vs Polycrystalline dislocation motion Twinning Parallel or Dislocation line Burger’s vector Slip plane Twin Plane Perpendicular? Types of Twinning Screw Dislocation Slipping vs Twinning dislocation ⊥ ⊥ II motion MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning screw edge dislocation line dislocation line Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline screw edge Twinning dislocation line dislocation line Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Here are some mechanisms of slip: Learning Outcomes Plastic Deformation Slipping Edge Edge, Screw, Mixed Stress Field Screw Slip along Atomic Planes Mixed Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Parallel or Dislocation line Burger’s vector Slip plane Types of Twinning Perpendicular? Slipping vs Twinning Mixed Dislocation dislocation Between 0 - 90° Between 0 - 90° Between 0 - 90° motion MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Stress Field in a Dislocation Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Stress Field in a Dislocation Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Stress Field in a Dislocation Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline addition Twinning (dislocation forest) Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Stress Field in a Dislocation Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline addition cancellation Twinning (dislocation forest) Twin Plane an existing dislocation impedes a moving dislocation which Types of Twinning results to an overall strengthening of the material Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Stress Field in a Dislocation Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline addition cancellation Twinning (dislocation forest) Twin Plane an existing dislocation impedes a moving dislocation which Types of Twinning results to an overall strengthening of the material Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip along Atomic Planes Slip occurs preferentially along high density planes and high Learning Outcomes density directions. Plastic Deformation Why? Slipping Edge, Screw, Mixed Slip occurs here because atom Stress Field displacement is a minimum! Slip along Atomic Planes Resolved Shear Stress D C Slipping of Single vs Polycrystalline Twinning Twin Plane B Types of Twinning Slipping vs Twinning A MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Systems Learning Outcomes Slip Plane preferred crystallographic planes where dislocations motion Plastic Deformation occurs Slipping Edge, Screw, Mixed Stress Field Slip Direction preferred crystallographic directions where dislocations Slip along Atomic Planes move Resolved Shear Stress Slipping of Single vs Polycrystalline Slip System Twinning combination of slip plane and slip direction Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Systems Learning Outcomes For FCC, Plastic Deformation Slipping Edge, Screw, Mixed High density atoms can be Stress Field found in the faces of the Slip along Atomic Planes cube. Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Slip plane: 111 Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Systems Learning Outcomes For FCC, Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Slip plane: 111 Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Systems Learning Outcomes For FCC, Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Slip plane: 111 # of slip systems: 4 × 3 = 𝟏𝟐 Types of Twinning Slip directions: 1ത 10 Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Systems Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  How do dislocations multiply? Learning Outcomes Frank- Read Source Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning A pinned dislocation segment bows out under an applied stress, forming a loop. As the loop expands, it eventually touches itself, creating two new dislocations. This process can be repeated, leading to a multiplication of dislocations. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  How do dislocations multiply? Learning Outcomes Frank- Read Source Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning A pinned dislocation segment bows out under an applied stress, forming a loop. As the loop expands, it eventually touches itself, creating two new dislocations. This process can be repeated, leading to a multiplication of dislocations. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Dislocation Climb Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Usually happens at higher temperature Slipping vs Twinning Diffusion governed MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  What type of stress causes slip? Only a shear stress resolved in the SLIP PLANE and along the Learning Outcomes SLIP DIRECTION will cause dislocation movement Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Resolved Shear Stress Learning Outcomes Plastic Deformation 𝜏𝑟𝑠𝑠 = (F/Ao ) cosΦ cosλ Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Critical Resolved Shear Stress Minimum shear stress required to initiate slip Learning Outcomes Plastic Deformation Material property that determines when yielding occurs Slipping Plastic deformation (yielding) occurs when Edge, Screw, Mixed resolved shear stress > CRSS Stress Field angle between the applied stress and the slip Slip along Atomic Planes direction Resolved Shear Stress Slipping of Single vs Polycrystalline 𝜏𝑟𝑠𝑠 = (F/A 𝜏𝑐𝑟𝑠𝑠 𝜎𝑦o ) cosΦ cosλ Twinning Twin Plane angle between the Types of Twinning applied stress and the normal of the slip plane Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Critical Resolved Shear Stress Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Consider a single crystal of BCC iron oriented such that a tensile stress is applied along a direction. a) Compute the resolved shear stress along a (110) plane and in a ഥ direction when a tensile stress of 52 MPa is applied. ഥ b) If slip occurs on a (110) plane and in a direction, and the critical resolved shear stress is 30 MPa, calculate the magnitude of the applied tensile stress necessary to initiate yielding. Given: Miller Index Tensile Stress Normal to the Note: For cubic structures, the direction Slip Plane (110) vector normal to (110) is. Slip Direction ഥ Requirement: 𝜏𝑟𝑠𝑠 Working Equation/s: MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Consider a single crystal of BCC iron oriented such that a tensile stress is applied along a direction. a) Compute the resolved shear stress along a (110) plane and in a ഥ direction when a tensile stress of 52 MPa is applied. ഥ b) If slip occurs on a (110) plane and in a direction, and the critical resolved shear stress is 30 MPa, calculate the magnitude of the applied tensile stress necessary to initiate yielding. Given: Solution: Miller Index Find φ (angle between 𝟎𝟏𝟎 and 𝟏𝟏𝟎 ) 𝑢1 𝑢2 + 𝑣1 𝑣2 + 𝑤1 𝑤2 Tensile Stress 𝜙 = 𝑐𝑜𝑠 −1 𝑢12 + 𝑣12 + 𝑤12 𝑢22 + 𝑣22 + 𝑤22 Normal to the Slip Plane (110) (0)(1) + (1)(1) + (0)(0) 𝜙 = 𝑐𝑜𝑠 −1 Slip Direction ഥ 02 + 12 + 02 12 + 120 + 02 𝜙 = 45° Requirement: 𝜏𝑟𝑠𝑠 Working Equation/s: MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Consider a single crystal of BCC iron oriented such that a tensile stress is applied along a direction. a) Compute the resolved shear stress along a (110) plane and in a ഥ direction when a tensile stress of 52 MPa is applied. ഥ b) If slip occurs on a (110) plane and in a direction, and the critical resolved shear stress is 30 MPa, calculate the magnitude of the applied tensile stress necessary to initiate yielding. Given: Solution: Miller Index Find λ (angle between 𝟎𝟏𝟎 and [𝟏𝟏𝟏]) 𝑢1 𝑢2 + 𝑣1 𝑣2 + 𝑤1 𝑤2 Tensile Stress λ = 𝑐𝑜𝑠 −1 𝑢12 + 𝑣12 + 𝑤12 𝑢22 + 𝑣22 + 𝑤22 Normal to the Slip Plane (110) (0)(−1) + (1)(1) + (0)(1) λ = 𝑐𝑜𝑠 −1 Slip Direction ഥ 02 + 12 + 02 −12 + 120 + 12 λ = 54.7° Requirement: 𝜏𝑟𝑠𝑠 Working Equation/s: MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Consider a single crystal of BCC iron oriented such that a tensile stress is applied along a direction. a) Compute the resolved shear stress along a (110) plane and in a ഥ direction when a tensile stress of 52 MPa is applied. ഥ b) If slip occurs on a (110) plane and in a direction, and the critical resolved shear stress is 30 MPa, calculate the magnitude of the applied tensile stress necessary to initiate yielding. Given: Solution: Miller Index Find 𝜏𝑟𝑠𝑠 Tensile Stress 𝞽𝑅𝑆𝑆 = 𝞼𝑌 𝑐𝑜𝑠𝟇𝑐𝑜𝑠𝞴 Normal to the Slip Plane (110) 𝞽𝑅𝑆𝑆 = (52)𝑐𝑜𝑠(45°)𝑐𝑜𝑠(54.7°) Slip Direction ഥ 𝞽𝑅𝑆𝑆 = 21.3 𝑀𝑃𝑎 Requirement: 𝜏𝑟𝑠𝑠 Working Equation/s: MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Consider a single crystal of BCC iron oriented such that a tensile stress is applied along a direction. a) Compute the resolved shear stress along a (110) plane and in a ഥ direction when a tensile stress of 52 MPa is applied. ഥ b) If slip occurs on a (110) plane and in a direction, and the critical resolved shear stress is 30 MPa, calculate the magnitude of the applied tensile stress necessary to initiate yielding. Given: 𝜏𝑐𝑟𝑠𝑠 = 30 𝑀𝑃𝑎 Solution: Miller Index 𝞽𝑪𝑹𝑺𝑺 = 𝞼𝒀 𝒄𝒐𝒔𝟇𝒄𝒐𝒔𝞴 Tensile Stress Normal to the 𝟑𝟎 𝑴𝑷𝒂 = 𝞼𝒀 𝒄𝒐𝒔(𝟒𝟓°)𝒄𝒐𝒔(𝟓𝟒. 𝟕°) Slip Plane (110) Slip Direction ഥ 𝞼𝒀 = 𝟕𝟑. 𝟒 𝑴𝑷𝒂 Requirement: 𝜎𝑦 Working Equation/s: MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip in Single Crystals vs Slip in Learning Outcomes Polycrystals Plastic Deformation Slip in single crystals is manifested macroscopically by slip Slipping lines on the surface of the material. Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning For polycrystalline materials, slip occurs within each grain. Twin Plane Types of Twinning Greater stresses are required to initiate slip and the Slipping vs Twinning attendant yielding Direction of slip varies from one grain to another. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Bands groups of closely spaced, parallel slip displacements that Learning Outcomes appear as single lines when observed under the optical Plastic Deformation microscope Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Manifestations of Slip Learning Outcomes https://www.youtube.com/watch?v=kzIsvbKHgfU Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip Systems Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Most HCP and FCC metals do not undergo slipping. Slipping vs Twinning Instead, their plastic deformations occur due to twinning. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Twinning Learning Outcomes Plastic Deformation occurs in the following conditions: conditions which restricts the possibility of SLIP Slipping low temperatures Edge, Screw, Mixed high rates of shear loading (shock loading) Stress Field Slip along Atomic Planes TWINNING occurs less frequently than SLIP Resolved Shear Stress Reason: Stress required is LARGE. Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Twinning Learning Outcomes occurs when crystals are stressed to form the defect called twin Plastic Deformation A surface/boundary defect that happens when the Slipping crystals on either side of a plane are mirror images of each other Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning https://www.youtube.com/watch?v=FPtHe8Su2RU MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Twinning There are two (2) types of twinning: Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Higher stacking fault energy Lower stacking fault energy Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip vs Twinning Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning Twin Plane Types of Twinning Slipping vs Twinning MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Slip vs Twinning Learning Outcomes Plastic Deformation Slipping Edge, Screw, Mixed Stress Field Slip along Atomic Planes Resolved Shear Stress Slipping of Single vs Polycrystalline Twinning The real importance of twinning lies with the accompanying Twin Plane crystallographic reorientations; twinning may place new slip Types of Twinning systems in orientations that are favorable relative to the Slipping vs Twinning stress axis such that the slip process can now take place. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Quiz Consider a single crystal of silver oriented such that a tensile stress is applied along a direction. If slip occurs on a (111) plane and in a [1ത 01] direction, and is initiated at an applied tensile stress of 1.1 MPa, compute the critical resolved shear stress. MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez  Quiz MatE 22 - Structure-Property Relationship of Materials II | JABNarvaez Thank You! References: Lecture adapted from previous MatE 22 classes (Maam Tiff Lao) MatE 22 Module 4 – Stresses and Deformation Callister, Jr., W. D. (2013). Materials Science and Engineering - An Introduction. New York: John Wiley & Sons, Inc. Askeland, D. R., Fulay, P. P., & Wright, W. J. (2016). The Science and Engineering of Materials 7th Ed. Stamford: Cengage Learning. MATE 22 - STRUCTURE-PROPERTY RELATIONSHIP OF MATERIALS II | JABNARVAEZ