Crystalline Slip: Flashcards and Quiz Flashcards

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Ideal Shear

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The ideal shear strength is the shear stress required to shear entire crystal planes simultaneously, representing the theoretical maximum cohesive strength of a perfect lattice. Simple estimates give values on the order of $\mu/2\pi$ (often quoted roughly as $\mu/6$), which are much larger than experimentally measured yield stresses due to defects like dislocations.

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Dislocation

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A dislocation is a line defect that separates slipped and unslipped regions on a crystallographic plane, allowing incremental shear instead of simultaneous shear of an entire plane. Dislocations dramatically reduce the applied stress required for plastic deformation compared to the ideal shear strength.

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Burgers Vector

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The Burgers vector $b$ specifies the magnitude and direction of lattice displacement produced by a dislocation and characterizes the amount of slip when the dislocation moves. It is fundamental to dislocation energetics, interactions, and the types of slip systems that operate.

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Peierls Stress

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Peierls stress $\tau_P$ is the critical shear stress needed to move a dislocation in a perfect crystal and depends strongly on bond strength, core width $w$, temperature $T$, and strain rate. Narrow cores and stronger bonds (e.g., ceramics/covalent) give larger $\tau_P$, while higher $T$ and lower strain rates lower $\tau_P$.

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Schmid Factor

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The Schmid factor $S$ quantifies resolved shear stress on a slip system and equals $S=\cos\lambda\cos\phi$, where $\lambda$ is angle between tensile axis and slip direction and $\phi$ between tensile axis and slip plane normal. The larger $S$, the easier that slip system is to activate under an applied tensile stress.

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Slip System

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A slip system consists of a slip plane and slip direction (e.g., {111}/<110> in FCC) on which dislocations glide most easily because of dense atomic packing. The number and geometry of active slip systems determine whether a crystal can accommodate arbitrary plastic deformation.

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Crystal Rotation

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During plastic deformation grains rotate as active slip systems operate, which changes Schmid factors and can activate new slip systems; this progressive rotation is a key mechanism of texture development. Rotation toward slip directions can cause overshoot behavior where primary and secondary systems alternate activity.

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Independent Slip Systems

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To produce arbitrary plastic strain while conserving volume, a polycrystal generally needs at least five independent slip systems. Materials (like many HCP metals) with fewer independent systems tend to be less ductile unless additional modes ( twinning or cross-slip) become available.

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FCC Slip Systems

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FCC crystals predominantly deform on close-packed {111} planes in <110> directions, giving 12 primary slip systems. This dense set of slip systems enables high ductility in FCC metals at typical temperatures.

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BCC Slip Systems

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BCC metals commonly slip on {110}/<111> planes and also on {112}/<111> or {123}/<111>, giving many potential systems (up to 48). Despite many systems, BCC dislocation core structures and Peierls barriers make low-temperature ductility more limited than FCC in some cases.

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HCP Slip

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HCP crystals often rely on basal {0001}, prismatic, and pyramidal slip systems; whether basal or prismatic slip dominates depends on the $c/a$ ratio and bonding across planes. Many HCP metals lack five independent slip systems, which contributes to limited ductility in polycrystals.

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Twinning

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Twinning is a crystallographic shear that produces a mirror-related region (twin) and can accommodate deformation when slip is insufficient. Twins nucleate in bursts, can create stacking faults, and are common in HCP metals and at low $T$ or high strain rates in BCC.

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Texture

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Texture describes preferred crystallographic orientations in a polycrystal that develop during deformation processes like rolling or drawing and is quantified by pole figures. Texture causes anisotropic mechanical responses (elastic and plastic) and is influenced by stacking fault energy and cross-slip activity.

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R-value

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The R-value quantifies anisotropic sheet-metal thinning during stretching; materials with larger average R resist thinning and are better for deep drawing. Randomly oriented grains give $R\approx1$, while strong texture can yield much larger $R$.

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Limited Drawing Ratio

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The limited drawing ratio (LDR) measures how deep a cup can be drawn from a blank and increases with higher R-values; higher LDR indicates better formability for deep drawing operations. Materials like titanium and some steels have large R and LDR, making them good forming candidates.

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Cross-Slip

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Cross-slip is the process where a screw dislocation changes its glide plane to bypass obstacles, enabling continued plastic flow. Cross-slip is easier when stacking-fault energy $\gamma_{sf}$ is large (small partial separation), giving narrower stacking faults and more frequent cross-slip.

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Climb

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Climb is a mechanism by which edge dislocations move out of their glide plane by absorbing or emitting vacancies, allowing them to bypass obstacles that cannot be surmounted by glide. Climb is diffusion-controlled and therefore becomes more significant at higher temperatures.

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Frank-Read Source

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A Frank-Read source is a dislocation multiplication mechanism where a pinned segment bows out under shear stress and forms dislocation loops, increasing dislocation density during plastic deformation. The stress required to operate a source increases as the spacing between pinning sites decreases.

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Stacking Fault Energy

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Stacking-fault energy (SFE) $\gamma_{sf}$ is the energy per area of a planar fault created by partial dislocation separation; low $\gamma_{sf}$ favors wide partial separation and planar slip. The equilibrium stacking-fault width scales approximately as $w_{sf} \approx \frac{\mu b^2}{2\pi\gamma_{sf}}$, so lower $\gamma_{sf}$ yields wider faults.