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Unformatted text preview: DEFORMATION & STRENGTHENING MECHANSISMS Plas%c deforma%on occurs on a macroscopic scale through the net movement of atoms as a result of an applied force. Basic Concepts Atomic mo%on through the movement of disloca%on structures is referred to as slip. The crystallographic plane along which slip occurs is called the slip plane. Basic Concepts The mo%on of edge and screw disloca%ons give rise to the same net change for a given shear force. However, note that atomic mo%on occurs in orthogonal direc%ons for the two different types of loca%ons. Basic Concepts Disloca%on mo%on can be envisioned as the net movement of a collec%on of atoms through a crystal laLce. In reality, the con4nual process of breaking and making of “bonds” leads to the observed deforma4on pa9erns. Characteris%cs of Disloca%ons The proper%es of disloca%ons can be characterized by the strain fields that exist within neighboring regions of the crystal structure (referred to as la'ce strain). Due to the physical difference in local atomic densi%es and geometries, regions of compressive and tensile stress will coexist in opposing regions. li − l0 Δl ε= = l0 l0 Characteris%cs of Disloca%ons Edge disloca%ons can be viewed as having a polarity or sign. As a result, individual disloca%ons will exhibit aRrac%ve or repulsive character. Note the use of the short hand nota%on to represent the presence and orienta%on of the edge disloca%on. Characteris%cs of Disloca%ons •  During plas%c deforma%on, the number of disloca%ons increases drama%cally. •  Disloca%on density in a deformed metal can be as high as 1010mm- 2 •  Exis%ng disloca%ons, grain boundaries, internal defects and surface irregulari%es are an important source of new disloca%ons. Slip Systems • The degree or extent of slip is anisotropic. It depends on the crystallographic direc%on in which slip occurs. • A slip system, the slip plane in combina%on with the slip direc4on, is used to describe slip in crystalline materials. • Slip is most favorable along planes of the highest atomic density. • Slip is most favorable along direc%ons of the highest atomic density. Slip Systems • Metals with FCC and BCC structures have rela%vely more slip systems than other crystal systems. • As a result, many such metals are duc%le. • HCP metals, with fewer slip systems, are observed to be rela%vely briRle. Indicates family of direc%ons related by symmetry Slip in single crystals Because stress is not always applied in the same orienta%on of a slip system, the component of the stress driving slip can be less than the total stress. This component is call the resolved shear stress (R) and is given by the equa%on: τ R = σ cosφ cos λ The angles are defined rela%ve to the direc%on of applied force, the slip plane, and the slip direc%on. The stress required to induce slip within a crystalline material is known as the cri3cal resolved shear stress (τcrss). 6-9 Slip in single crystals Slip will occur as the result of either compressive or tensile stresses and will occur for the slip system of the largest resolved shear stress (can be calculated for each slip system). Deforma%on of a single crystal: example Q: Will this single crystal yield? φ = 60° λ = 35° σ = 45 MPa τcrss = 20.7 MPa Deforma%on of a single crystal: example Will this single crystal yield? φ = 60° λ = 35° τcrss = 20.7 MPa τ = σ cos λ cos φ σ = 45 MPa € σ = 45 MPa τ = (45 MPa) ( cos 35 )(cos 60 ) = (45 MPa) (0.41) τ = 18.4 MPa < τ crss = 20.7 MPa So the applied stress of 45 MPa will not cause the crystal to yield. Slip mo%on in polycrystals • Polycrystals stronger than single crystals – grain boundaries are barriers to dislocation motion. • Slip planes & directions (λ, φ) change from onegrain to another. • τR will vary from onegrain to another. • The grain with the largest τR yields first. • Other (less favorablyoriented) grains yield later. Even though a single grain may be favorably aligned with the applied stress for slip, it cannot deform un4l the adjacent, less favorably aligned grains are also capable of slip. This requires a higher applied stress. σ Mechanisms of strengthening in metals We will compare and contrast three mechanisms by which metals can be strengthened. •  Strengthening by Grain Size Reduc3on •  Solid Solu3on Strengthening •  Strain Hardening Strengthening: Grain size reduc%on •  The grain size found in polycrystalline metals is strongly a func%on of processing. •  Grain boundaries are barriers to slip. •  The origin of this effect is related to the energy dissipated when disloca%on mo%on changes direc%on at a grain boundary. •  Smaller grains = more barriers to slip. •  The yield strength of many metals is related to the grain size through the Hall- Petch equa4on, in which σo and κy are materials specific constants. σ y = σ o + kyd −1 2 Strengthening: Grain size reduc%on Note that increases in strength can be significant. σ y = σ o + kyd −1 2 Strengthening: Solid solu%on The alloying of metals leads to the localized introduc%on of either tensile or compressive strain. The existence of subs%tu%onal or inters%%al species can also play a role in stabilizing edge or screw disloca%ons, thus effec%vely increasing the strength of the material. 6-17 Strengthening: Solid solu%on 400 300 200 0 10 20 30 40 50 wt.% Ni, (Concentration C) Yield strength (MPa) Tensile strength (MPa) Consider the data below measured as a func%on of increasing Ni content in a CuNi alloy. 180 120 60 0 10 20 30 40 50 wt.%Ni, (Concentration C) Strengthening: Strain hardening •  Strain hardening refers to the increase in strength (or hardness) that occurs in metals as a result of plas%c deforma%on. It is some%mes referred to as work hardening. •  The origin of the effect lies in the increase in disloca4on density with increasing plas4c deforma4on. The increase in number effec%vely restricts disloca%on mo%on. •  The mo4on of a disloca4on is hindered by the presence of other disloca4ons •  The degree of plas%c deforma%on can be expressed as percent cold work (%CW). ( Ao − Ad ) ×100 %CW = Ao Strengthening: Strain hardening •  Increase in strength (or hardness) occurs in metals as a result of plas%c deforma%on •  Deforma%on at room temperature (for most metals). •  Common forming opera%ons reduce the cross- sec%onal area: -Forging force -Rolling die A o blank roll Ao Ad Ad roll force -Extrusion -Drawing die Ao die Ad Ao tensile force force container ram billet container Ao − Ad %CW = x 100 Ao die holder extrusion die Ad Strengthening: Strain hardening The increase in hardness typically is accompanied by a reduc%on in duc%lity – ie. the metal becomes more bri9le. Strengthening: Strain hardening The influence of cold working, or strain hardening, is evident in stress- strain data recorded as a func%on of %CW. Mechanical proper%es: Cold working example What are the values of yield strength, tensile strength, & duc%lity acer cold working Cu as shown below? Copper Cold Work Do = 15.2 mm Dd = 12.2 mm Mechanical proper%es: Cold working example What are the values of yield strength, tensile strength, & duc%lity acer cold working Cu as shown below? Ao − Ad %CW = x 100 Ao 2 2 πDo πDd − 4 x 100 %CW = 4 2 πDo 4 Copper Cold Work Do = 15.2 mm %CW = Dd = 12.2 mm (15.2 mm)2 − (12.2 mm)2 (15.2 mm)2 = 2 2 Do − Dd 2 Do x 100 x 100 = 35.6% Mechanical proper%es: Cold working example 500 300 300 MPa 100 0 20 40 Cu % Cold Work 60 σy = 300 MPa 60 800 ductility (%EL) 700 tensile strength (MPa) yield strength (MPa) What are the values of yield strength, tensile strength & duc%lity for Cu for %CW = 35.6%? 600 400 340 MPa 200 0 20 Cu 40 60 40 20 Cu 7% 0 0 20 40 60 % Cold Work % Cold Work TS = 340 MPa %EL = 7% Recovery, Recrystalliza%on & Grain Growth A cold worked metal that is heat treated may experience a degree of recovery, recrystalliza4on and grain growth, altering its proper4es. Recovery At elevated temperatures, enhanced atomic diffusion will enhance disloca%on mo%on, and thus par%ally relieve a por%on of the internal strain energy stored during cold working. This process is known as recovery and results in a reduc4on of the number of disloca4ons. Recrystalliza3on Extended exposure at sufficiently high temperature will lead to the forma%on of new, more equiaxed grains, the process of recrystalliza3on. Disloca4on densi4es are lowered even further. These processes are strongly dependent on %me and temperature. Recovery, Recrystalliza%on & Grain Growth 1) 33%CW: Pre- hea%ng 2) Recrystalliza%on begins 5) Early grain growth stage 3) Par%cal replacement of 4) Complete recrystalliza%on CW grains by recrystallized grains 6) Late grain growth stage Recovery, Recrystalliza%on & Grain Growth Recovery, Recrystalliza%on & Grain Growth The recrystalliza3on temperature is defined as the temperature in which recrystalliza%on is complete in 1 hour %me. This temperature is typically 1/3 to 1/2 the mel%ng temperature. Reminder: Recrystalliza%on is driven by an energy change, effec%vely relieving energy induced by the cold working of a metal. Below a certain %CW, recrystalliza%on will not occur (~2- 20%). Recovery, Recrystalliza%on & Grain Growth Grain Growth: As the name implies, prolonged exposure to elevated temperatures leads to a con%nued increase in grain size Summary •  The mechanical proper%es of metals are strongly dependent on the nature of internal defects. •  The mechanical proper%es of metals can be influenced by the purposeful introduc%on of defects. •  Temperature is seen as a means of relieving internal strain and altering internal defect structures. ...
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