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Dislocation glide in a hexagonal crystal on its basal $(0001)$ plane, ordinarily along a close-packed basal direction in the $⟨11\overline{2}0⟩$ family. Direction indices must be converted using the actual hexagonal metric, including the ratio $c/a$.

Motion of an edge component perpendicular to its glide plane by absorbing or emitting point defects. Unlike conservative dislocation glide, it changes the extra-plane content locally and is coupled to defect transport. Irradiation can drive climb by creating nonequilibrium vacancies and self-interstitials.

A line segment formed by interaction of dislocations from different slip planes. A junction can impede further dislocation glide. Energetic favourability alone does not establish whether the resulting segment is mobile on a particular plane.

Resistance to dislocation glide produced by intersections with other dislocations. Multiple active slip systems can form junctions and increase the density of obstacles. This is one mechanism of work hardening.

An increase in resistance to plastic flow caused by irradiation-produced obstacles to dislocation glide, including loops, clusters and precipitates. Increased strength can coexist with reduced ductility.

The alloy shear yield stress can be roughly $70/0.78\simeq 90$ times the stated pure-aluminium critical resolved shear stress. Strengthening raises the stress required for dislocation glide rather than requiring homogeneous shearing of a perfect crystal.

These mechanisms can coexist. The numerical comparison is an order-of-magnitude comparison of shear strengths; it is not a conversion of the alloy's shear yield stress directly into a tensile yield stress.

Material creep is time-dependent permanent deformation under sustained stress. Its rate is often appreciable at a large homologous temperature $T/T_m$, because diffusion and obstacle-escape processes become rapid. In an activated regime a useful form iswith additional elastic, geometric and temperature prefactors absorbed into $A$ for the chosen approximation. The activation energy belongs to the rate-controlling process: bulk diffusion, grain-boundary diffusion and dislocation motion need not have the same value.

Boundary sliding can accommodate grain-shape changes during diffusional material creep; it is not a reason to identify either diffusion field as dislocation glide. The supplied map's A/B/C placement, including the boundary between B and C, determines these assignments. Its numerical contours apply to the material state used to construct that map, not to arbitrary grain sizes.

Initially, one slip system carries most of the deformation. Easy dislocation glide gives the nearly flat stage-I response, although lattice rotation and gradual dislocation interactions can already change the required tensile stress. In tension the loading direction expressed in the rotating crystal approaches the primary slip direction. Its path has the form $(5+t,1+t,4)$ until it reaches the symmetry boundary $y=z$, at $[844]=[211]$.

At that orientation, $(1\bar{1}1)[110]$ and $(11\bar{1})[101]$ have equal Schmid factors, $1/\sqrt{6}$. Conjugate slip therefore becomes competitive. Intersections between the two dislocation families generate obstacles, junctions and forest hardening, giving the sharp stage-II rise in flow stress. This is the ideal single-slip-to-conjugate-slip construction; real activation stresses can be shifted by latent hardening and imperfections.

The annealed sample initially has relatively few obstacles to dislocation glide. After its elastic response it yields, undergoes appreciable plastic deformation and develops strain hardening. Irradiation produces dislocation loops and defect clusters that obstruct gliding dislocations, usually raising the yield strength. In a simple dispersed-obstacle model the strengthening scales as $\Delta \sigma \sim M\alpha Gb\sqrt{Nd}$, with obstacle density $N$ and diameter $d$.

Irradiated material often has less uniform plastic elongation and weaker subsequent hardening because slip localizes into channels that have cleared irradiation obstacles. Earlier necking or fracture can then reduce ductility. The elastic slope is much less affected than the yield stress in this schematic comparison; the exact strength and elongation depend on dose and temperature.

As-quenched martensite generally has greater hardness and strength, but lower ductility and toughness, than ordinary pearlitic steel. Its supersaturated carbon and distorted lattice impede dislocation glide; quench stresses also promote cracking. Pearlite combines hard cementite lamellae with more deformable ferrite, with finer spacings generally giving greater strength. Austenitize, quench to martensite, then temper to obtain a useful compromise between indentation resistance and resistance to fast fracture. Tempering below the austenitizing range relieves stresses and develops a fine carbide-containing microstructure. It trades some maximum hardness for improved toughness; the temperature and time must suit the required balance.

The exponential in the Peierls stress makes a large core-width-to-Burgers vector ratio $w/b$ favourable for easy dislocation glide. Densely packed slip planes often have wider cores because the shear distortion can spread over more atomic rows, reducing the lattice-periodic barrier. Close-packed directions provide short lattice translations and hence small allowed Burgers vectors; their line energies, approximately proportional to $G{b}^2$, are also relatively low. These effects favour dense planes and directions, but the relation between packing and core width is a physical argument rather than a consequence of substituting arbitrary independent $w,b$ into the formula. Body-centred cubic metals have densely packed directions without a truly close-packed plane, and their screw-core behaviour can require additional qualifications.

The cosine of the angle between Burgers vector and line direction is $1/3$, so the angle is $70.53^{\circ }$: the dislocation is mixed. Both vectors must lie in its dislocation glide plane. Their cross product is proportional toso the plane is $(10\bar{1})$, a member of $\{110\}$. The screw component magnitude is $a/(2\sqrt{3})$ and the edge component magnitude is $a\sqrt{2/3}$.

The characteristic effect is an irradiation-induced upward shift of the ductile-to-brittle transition in ferritic steel. A component previously used above its transition can then fail by cleavage fracture at the same service temperature, with much less warning from plastic deformation.

Ferrite has a body-centered cubic lattice. At low temperature, dislocation glide becomes difficult enough that brittle crack propagation can precede substantial plastic relaxation. Irradiation hardening raises the yield strength by introducing obstacles to dislocation glide; the competition with cleavage fracture consequently shifts toward brittle failure. Austenite, with its face-centered cubic lattice, does not normally show this same sharp cleavage transition. This does not make austenitic steel immune to loss of ductility, helium embrittlement or other radiation damage in materials.

Examine the fracture surface for cleavage fracture facets and river patterns, and compare Charpy impact test energy-versus-temperature curves from exposed material and an unirradiated reference of the same composition and heat treatment. The reference is important: a low impact energy from one failed specimen cannot establish an irradiation-induced shift. Transition curves can also use lateral expansion or the proportion of ductile fracture appearance.^[ref]

A direct fracture toughness test over the transition region complements the Charpy impact test; the two measurements are not interchangeable. Combine these observations with exposure history, local temperature, microstructure and crack location. Brittle appearance supports the failure mechanism, while a measured transition shift and suitable controls support its attribution to irradiation.

Irradiation softening occurs when irradiation removes pre-existing strengthening obstacles faster than it creates new ones. It is particularly plausible in an initially hardened alloy, rather than an initially soft annealed reference.

In a material strengthened by cold working, the starting dislocation density is high. Irradiation-generated point defects can assist dislocation climb, rearrangement and annihilation, reducing the contribution of work hardening. A schematic estimate iswhere $\mu$ is the shear modulus, $b$ the magnitude of the Burgers vector, ${\rho }_d$ the dislocation density, and the last two terms represent precipitate and irradiation-obstacle strengthening. It is an illustrative decomposition, not an exact additive law for every alloy. A sufficiently large decrease in the pre-existing contributions can exceed the increase in $\Delta {\sigma }_{\mathrm{irr}}$.

In a material strengthened by precipitation hardening, ballistic mixing can dissolve or disorder the original obstacles. Radiation-enhanced diffusion can change their composition or accelerate coarsening; increasing obstacle spacing can reduce strength. In an ordered alloy, irradiation-induced loss of order can also remove a strengthening contribution. None of these outcomes is inevitable: irradiation can instead create new strengthening precipitates.

The required conditions therefore include an appropriate initial microstructure, enough displacement dose to modify it, and a temperature and displacement dose rate at which obstacle removal or recovery can compete with new defect accumulation. Compare with an unirradiated specimen held for the same time at the same temperature to separate ordinary thermal aging from an irradiation effect.

A drop in yield strength or hardness need not restore ductility: cavities, helium embrittlement or localization of dislocation glide can coexist with softening. Conversely, an initially annealed steel may show strong irradiation hardening under the same exposure conditions.

Irradiation creep adds stress-directed, time-dependent strain driven by the irradiation-generated defect population. It can be appreciable where ordinary thermal material creep would be slow, because irradiation maintains mobile point defects far above their equilibrium populations.

Absorption or emission of vacancies and self-interstitials permits dislocation climb. Applied stress can make differently oriented dislocations or dislocation loops absorb defects at different rates: stress-induced preferential absorption then produces a directional strain. Climb can also allow a pinned dislocation to bypass an obstacle and continue dislocation glide, providing a second route to strain.

A useful small-strain empirical form, over a limited range of conditions, isfor constant stress $\sigma$ and approximately constant irradiation-creep compliance $B$. Here $d$ is the accumulated displacements per atom and $\dot{d}$ the displacement dose rate; $B$ is measured per unit stress and per unit dpa. This relation explains why creep can scale approximately with both stress and neutron flux when the damage spectrum is fixed. It is not a constitutive law valid at every dose or temperature.

The total strain can also include thermal material creep, void swelling, irradiation growth and changes due to precipitation or recovery. Stress-free swelling is not itself irradiation creep. Experiments on pressurized type316 tubes separated these contributions and found that correcting stress-enhanced swelling materially affected comparisons between annealed and specimens strengthened by cold working.^[ref]

At sufficiently high temperature, thermal material creep can dominate. Changes in microstructure caused by irradiation hardening, softening, bubbles and cavities can either alter the creep rate or shorten rupture life. Thus enhanced defect-driven creep is the central effect, while the net rate and lifetime remain material- and history-dependent.

The low-temperature zirconium matrix has a hexagonal close packing structure. Its crystallographic $a$ and $c$ directions therefore have different elasticity, thermal expansion and available slip systems. Producing tubing also develops a crystallographic texture, so averaging over grains does not necessarily remove these directional effects.

Different expansion along the crystal axes produces intergranular thermal stresses during temperature changes. Under load, easy dislocation glide modes may accommodate some strains much more readily than others; additional slip or crystal twinning is needed for general compatibility. Consequently strength and ductility can depend on the axial, circumferential and radial orientation of the tube.

Irradiation creates vacancies and self-interstitials that cluster into dislocation loops with different crystallographic orientations. Their anisotropic accumulation can produce irradiation growth even without external stress. Different directions can elongate or contract while the net volume change remains small. Texture turns these grain-scale strains into macroscopic length and diameter changes, bowing and stresses between constrained components. This mechanism is distinct from the added cavity volume of void swelling.

The crystallographic character of irradiation loops matters: atomistic calculations by Rory Hulse and Christopher P. Race examine several possible loop types and show that loop energy and shape depend on orientation and size. A single generic spherical-defect description therefore misses important aspects of zirconium's dimensional response.^[ref]

Hydrogen also produces direction-sensitive damage. Zirconium hydrides are brittle precipitates whose preferred orientation depends on crystal texture and stress history. Radially oriented hydrides can offer crack paths across a thin tube wall under circumferential tension. Controlling texture, hydrogen pickup and hydride orientation helps manage that risk; changing the hexagonal structure's orientation cannot by itself eliminate corrosion or irradiation damage.

A lattice-friction stress for dislocation glide, associated with Rudolf Peierls and Frank Nabarro. A simple model gives ${\tau }_P\sim 3G\exp (-2\pi w/b)$, where $w$ is core width and $b$ the Burgers vector magnitude. Spreading slip over many atomic rows reduces the periodic energy barrier; narrower cores are harder to move in this model.

A crystallographic plane together with an allowed dislocation glide direction in that plane. Geometry alone does not determine its activation stress.

An increase in resistance to further plastic deformation after deformation has changed the microstructure. Increasing dislocation density and interactions can impede subsequent dislocation glide.