Mechanisms of Plastic Deformation and Slip

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plastic-deformation dislocation-motion slip

Core Idea

Plastic deformation occurs through dislocation motion along slip planes and slip directions (slip systems), allowing permanent shape changes at applied stresses much lower than predictions from ideal crystal strength. Slip systems are defined by crystallography and vary with crystal structure (FCC, BCC, HCP metals have different numbers and orientations of slip systems). Work hardening occurs as dislocation density increases during deformation, increasing strength but decreasing ductility.

Explainer

From your study of elastic deformation and dislocations, you know two things: first, elastic deformation is reversible stretching of atomic bonds; second, real crystals contain line defects called dislocations where the crystal lattice is locally disrupted. These two ideas connect here: plastic deformation is permanent shape change caused not by bond rupture across an entire plane, but by the motion of dislocations through the crystal one atomic row at a time.

To see why dislocation motion is so important, consider the theoretical shear stress required to slide one entire atomic plane across another simultaneously. Calculations based on atomic bond strengths give a theoretical shear strength of roughly G/10 to G/30 (where G is the shear modulus). In practice, metals yield at stresses thousands of times lower than this — the measured yield shear stress for pure copper is about G/10,000. The resolution is that dislocations allow planes to slip incrementally, not all at once. Each dislocation sweeps across the slip plane one atom at a time, like a wrinkle moving across a carpet: the wrinkle requires much less force to advance than lifting the entire carpet. The cumulative effect of many dislocations traversing the crystal produces a macroscopic permanent strain.

Dislocations do not move on arbitrary planes. They are confined to specific crystallographic slip systems — combinations of a slip plane (typically the most densely packed plane) and a slip direction (the closest-packed direction). FCC metals like aluminum and copper have 12 equivalent {111}⟨110⟩ slip systems, giving them excellent ductility because there are many ways for dislocations to move. BCC metals like iron have more slip systems but less closely packed planes, making slip harder and giving BCC metals higher strength and lower ductility than FCC at room temperature. HCP metals like magnesium have few independent slip systems, severely limiting ductility and making them brittle unless deformation twins supplement slip. Schmid's law quantifies this: the resolved shear stress on a slip system is τ = σ cos φ cos λ, where φ and λ are the angles between the loading axis and the slip plane normal and slip direction. Slip occurs when this resolved stress reaches the critical resolved shear stress (CRSS), a material constant.

Work hardening — the increase in strength that occurs during plastic deformation — follows naturally from this picture. As dislocations multiply and move, they encounter and tangle with each other. Each intersection creates a jog or a sessile dislocation segment that acts as a pinning point for subsequent dislocation motion. The more deformation the material has undergone, the higher the dislocation density, and the harder it becomes for additional dislocations to move through the forest of obstacles. The material strengthens, but because dislocation motion is being suppressed, the capacity for further deformation (ductility) decreases. This tradeoff — strength gained at the cost of ductility — is the defining characteristic of cold work and the starting point for understanding yield strength and tensile properties.

Practice Questions 5 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesThe Electromagnetic SpectrumBlackbody Radiation and Planck's LawPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthHeisenberg Uncertainty PrincipleWavefunction and the Born RuleThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsScattering TheoryIntroduction to Scattering TheoryPartial Wave Analysis in ScatteringSpin Angular MomentumElectron Spin and Intrinsic Magnetic MomentStern-Gerlach Experiment: Spin Quantization and MeasurementElectron Diffraction and Matter Wave PropertiesDavisson-Germer Experiment: Crystal Diffraction of ElectronsElectron Diffraction and Matter Wave InterferenceWavefunctions and Probability Density InterpretationQuantum Superposition and Linear Combinations of StatesQuantum Operators and ObservablesCanonical Commutation Relations and UncertaintyHeisenberg Uncertainty Principle and Measurement LimitsTime-Independent Schrödinger Equation and EigenvaluesHydrogen Atom in Quantum MechanicsSpectral Lines and Energy TransitionsSelection Rules for Atomic TransitionsLS and jj Coupling Schemes in Multi-Electron AtomsPauli Exclusion Principle and Antisymmetric WavefunctionsElectron Configuration and the Aufbau PrincipleThe Periodic Table and Atomic Electronic StructureThe Periodic TableElectron ConfigurationPeriodic TrendsIonization EnergyIonic BondingMetallic BondingAtomic Bonding in SolidsCrystal Systems and Bravais LatticesPoint Defects: Vacancies, Interstitials, and ImpuritiesDislocations: Types and MovementMechanisms of Plastic Deformation and Slip

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