In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. It is a material property that quantifies its ability to resist crack propagation and failure under applied stress. A component's thickness affects the constraint conditions at the tip of a crack with thin components having plane stress conditions, leading to ductile behavior and thick components having plane strain conditions, where the constraint increases, leading to brittle failure. Plane strain conditions give the lowest fracture toughness value which is a material property. The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the plane strain fracture toughness, denoted . When a test fails to meet the thickness and other test requirements that are in place to ensure plane strain conditions, the fracture toughness value produced is given the designation .
Slow self-sustaining crack propagation known as stress corrosion cracking, can occur in a corrosive environment above the threshold (Stress Corrosion Cracking Threshold Stress Intensity Factor) and below . Small increments of crack extension can also occur during fatigue crack growth, which after repeated loading cycles, can gradually grow a crack until final failure occurs by exceeding the fracture toughness.
Material variation Material typeMaterialKIc (MPa·m1/2)MetalAluminum 14–28Aluminum alloy (7075) 20–35Inconel 718 73–87Maraging steel (200 Grade) 175Steel alloy (4340) 50Titanium alloy 84–107CeramicAluminum oxide 3–5Silicon carbide 3–5Soda-lime glass 0.7–0.8Concrete 0.2–1.4 PolymerPolymethyl methacrylate 0.7–1.60Polystyrene 0.7–1.1 CompositeMullite-fibre composite 1.8–3.3Silica aerogels 0.0008–0.0048 Fracture toughness varies by approximately 4 orders of magnitude across materials. Metals hold the highest values of fracture toughness and ceramics holds the lowest. Cracks cannot easily propagate in tough materials, making metals highly resistant to cracking under stress and gives their stress–strain curve a large zone of plastic flow. Even though ceramics have a lower fracture toughness they show an exceptional improvement in the stress fracture that is attributed to their 1.5 orders of magnitude strength increase, relative to metals. The fracture toughness of composites, made by combining engineering ceramics with engineering polymers, greatly exceeds the individual fracture toughness of the constituent materials.
Mechanisms Intrinsic mechanisms Intrinsic toughening mechanisms are processes which act ahead of the crack tip to increase the material's toughness. These mechanisms operate at the atomic or microscopic level and are fundamental to the material itself, rather than being influenced by external factors. These will tend to be related to the structure and bonding of the base material, as well as microstructural features and additives to it. Examples of mechanisms include: crack deflection by secondary phases, crack separation due to fine grain structure changes in the crack path due to grain boundaries
Any alteration to the base material which increases its ductility can also be thought of as intrinsic toughening.
Grain boundaries The presence of grains in a material can also affect its toughness by affecting the way cracks propagate. In front of a crack, a plastic zone can be present as the material yields. Beyond that region, the material remains elastic. The conditions for fracture are the most favorable at the boundary between this plastic and elastic zone, and thus cracks often initiate by the cleavage of a grain at that location.
At low temperatures, where the material can become completely brittle, such as in a body-centered cubic (BCC) metal, the plastic zone shrinks away, and only the elastic zone exists. In this state, the crack will propagate by successive cleavage of the grains. At these low temperatures, the yield strength is high, but the fracture strain and crack tip radius of curvature are low, leading to a low toughness.
Additionally, the lack of plastic deformation at low temperatures results in minimal energy absorption before fracture, making the material highly susceptible to sudden and catastrophic failure. This brittle behavior is particularly critical in structural applications, where impact loading or stress concentrations can rapidly initiate fracture. The ductile-to-brittle transition temperature (DBTT) defines the temperature below which a material exhibits this brittle nature, and in BCC metals, it varies based on factors such as impurity content, grain size, and alloying elements. Engineering solutions, such as grain refinement or controlled heat treatments, are often employed to lower the DBTT and improve low-temperature toughness. Furthermore, external factors like strain rate and triaxial stress states can exacerbate brittleness, making careful material selection crucial for applications operating in cold environments.
At higher temperatures, the yield strength decreases, and leads to the formation of the plastic zone. Cleavage is likely to initiate at the elastic-plastic zone boundary, and then link back to the main crack tip. This is usually a mixture of cleavages of grains, and ductile fracture of grains known as fibrous linkages. The percentage of fibrous linkages increase as temperature increases until the linkup is entirely fibrous linkages. In this state, even though yield strength is lower, the presence of ductile fracture and a higher crack tip radius of curvature results in a higher toughness.
Additionally, the increased plasticity at elevated temperatures enhances energy dissipation during crack propagation, further improving material toughness. The transition from brittle to ductile fracture is also influenced by strain rate and microstructural factors, such as grain size and phase composition. Materials with finer grains tend to exhibit higher resistance to crack initiation due to increased grain boundary interactions. Furthermore, oxidation effects at high temperatures can play a role in altering crack behavior, either enhancing or reducing toughness depending on the material and environmental conditions.
Inclusions Inclusions in a material such as a second phase particles can act similar to brittle grains that can affect crack propagation. Fracture or separation at an inclusion can occur either due to external stress or because of dislocations that form as the inclusion tries to stay connected with the surrounding material. Similar to grains, the fracture is most likely to occur at the plastic-elastic zone boundary. Then the crack can linkup back to the main crack. If the plastic zone is small or the density of the inclusions is small, the fracture is more likely to directly link up with the main crack tip. If the plastic zone is large, or the density of inclusions is high, additional inclusion fractures may occur within the plastic zone, and linkup occurs by progressing from the crack to the closest fracturing inclusion within the zone.
Transformation toughening
Transformation toughening is a phenomenon whereby a material undergoes one or more martensitic (displacive, diffusionless) phase transformations which result in an almost instantaneous change in volume of that material. This transformation is triggered by a change in the stress state of the material, such as an increase in tensile stress, and acts in opposition to the applied stress. Thus when the material is locally put under tension, for example at the tip of a growing crack, it can undergo a phase transformation which increases its volume, lowering the local tensile stress and hindering the crack's progression through the material. This mechanism is exploited to increase the toughness of ceramic materials, most notably in Yttria-stabilized zirconia for applications such as ceramic knives and thermal barrier coatings on jet engine turbine blades.
A similar toughening process, albeit without volume change, can occur in materials in which the crystallographic unit cell can change its orientation due to an external load. In this case the crack-tip stress field will result in unit cells to re-align in the tensile stress direction, thus reducing the tensile stress. Since this process does not include a crystallographic phase transition, the unit cell volume remains constant. A good example of such behavior is found in soft lead zirconate titanate piezo-ceramics. Unlike in a traditional phase transformation, this process is in general reversible. Also, the original orientation of the unit cell is critical as the toughening effect cannot occur if the unit cell is already aligned with the tensile stress direction.
Extrinsic mechanisms Extrinsic toughening mechanisms are processes which act behind the crack tip to resist its further opening. Examples include fibre/lamella bridging, where these structures hold the two fracture surfaces together after the crack has propagated through the matrix, crack wedging from the friction between two rough fracture surfaces, and microcracking, where smaller cracks form in the material around the main crack, relieving the stress at the crack tip by effectively increasing the material's compliance.
Test methods Fracture toughness tests are performed to quantify the resistance of a material to failure by cracking. Such tests result in either a single-valued measure of fracture toughness or in a resistance curve. Resistance curves are plots where fracture toughness parameters (K, J etc.) are plotted against parameters characterizing the propagation of crack. The resistance curve or the single-valued fracture toughness is obtained based on the mechanism and stability of fracture. Fracture toughness is a critical mechanical property for engineering applications. There are several types of test used to measure fracture toughness of materials, which generally utilise a notched specimen in one of various configurations. A widely utilized standardized test method is the Charpy impact test whereby a sample with a V-notch or a U-notch is subjected to impact from behind the notch. Also widely used are crack displacement tests such as three-point beam bending tests with thin cracks preset into test specimens before applying load.
Testing requirements Choice of specimen The ASTM standard E1820 for the measurement of fracture toughness recommends three coupon types for fracture toughness testing, the single-edge bending coupon [SE(B)], the compact tension coupon [C(T)] and the disk-shaped compact tension coupon [DC(T)]. Each specimen configuration is characterized by three dimensions, namely the crack length (a), the thickness (B) and the width (W). The values of these dimensions are determined by the demand of the particular test that is being performed on the specimen. The vast majority of the tests are carried out on either compact or three-point flexural test configuration. For the same characteristic dimensions, compact configuration takes a lesser amount of material compared to three-point flexural test.
Material orientation