Creep (deformation)
In materials science, creep is the tendency of a solid material to undergo slow deformation while subject to persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increases as they near their melting point.
The rate of deformation is a function of the material's properties, exposure time, exposure temperature and the applied structural load. Depending on the magnitude of the applied stress and its duration, the deformation may become so large that a component can no longer perform its function – for example creep of a turbine blade could cause the blade to contact the casing, resulting in the failure of the blade. Creep is usually of concern to engineers and metallurgists when evaluating components that operate under high stresses or high temperatures. Creep is a deformation mechanism that may or may not constitute a failure mode. For example, moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that might otherwise lead to cracking.
Unlike brittle fracture, creep deformation does not occur suddenly upon the application of stress. Instead, strain accumulates as a result of long-term stress. Therefore, creep is a "time-dependent" deformation.
Creep or cold flow is of great concern in plastics. Blocking agents are chemicals used to prevent or inhibit cold flow. Otherwise rolled or stacked sheets stick together.
Temperature dependence
The temperature range in which creep deformation occurs depends on the material. Creep deformation generally occurs when a material is stressed at a temperature near its melting point. While tungsten requires a temperature in the thousands of degrees before the onset of creep deformation, lead may creep at room temperature, and ice will creep at temperatures below. Plastics and low-melting-temperature metals, including many solders, can begin to creep at room temperature. Glacier flow is an example of creep processes in ice. The effects of creep deformation generally become noticeable at approximately 35% of the melting point for metals and at 45% of melting point for ceramics.Theoretical framework
Creep behavior can be split into three main stages.In primary or transient creep, the strain rate is a function of time. In Class M materials, which include most pure materials, primary strain rate decreases over time. This can be due to increasing dislocation density, or it can be due to evolving grain size. In class A materials, which have large amounts of solid solution hardening, strain rate increases over time due to a thinning of solute drag atoms as dislocations move.
In the secondary, or steady-state, creep, dislocation structure and grain size have reached equilibrium, and therefore strain rate is constant. Equations that yield a strain rate refer to the steady-state strain rate. Stress dependence of this rate depends on the creep mechanism.
In tertiary creep, the strain rate exponentially increases with stress. This can be due to necking phenomena, internal cracks, or voids, which all decrease the cross-sectional area and increase the true stress on the region, further accelerating deformation and leading to fracture.
Mechanisms of deformation
Depending on the temperature and stress, different deformation mechanisms are activated. Though there are generally many deformation mechanisms active at all times, usually one mechanism is dominant, accounting for almost all deformation.Various mechanisms are:
- Bulk diffusion
- Grain boundary diffusion
- Glide-controlled dislocation creep: dislocations move via glide and climb, and the speed of glide is the dominant factor on strain rate
- Climb-controlled dislocation creep: dislocations move via glide and climb, and the speed of climb is the dominant factor on strain rate
- Harper–Dorn creep: a low-stress creep mechanism in some pure materials
Deformation mechanism maps
Deformation mechanism maps provide a visual tool categorizing the dominant deformation mechanism as a function of homologous temperature, shear modulus-normalized stress, and strain rate. Generally, two of these three properties are the axes of the map, while the third is drawn as contours on the map.To populate the map, constitutive equations are found for each deformation mechanism. These are used to solve for the boundaries between each deformation mechanism, as well as the strain rate contours.
Deformation mechanism maps can be used to compare different strengthening mechanisms, as well as compare different types of materials.
where ε is the creep strain, C is a constant dependent on the material and the particular creep mechanism, m and b are exponents dependent on the creep mechanism, Q is the activation energy of the creep mechanism, σ is the applied stress, d is the grain size of the material, k is the Boltzmann constant, and T is the absolute temperature.
Dislocation creep
At high stresses, creep is controlled by the movement of dislocations.For dislocation creep, Q = Q, 4 ≤ m ≤ 6, and b < 1. Therefore, dislocation creep has a strong dependence on the applied stress and the intrinsic activation energy and a weaker dependence on grain size. As grain size gets smaller, grain boundary area gets larger, so dislocation motion is impeded.
Some alloys exhibit a very large stress exponent, and this has typically been explained by introducing a "threshold stress," σth, below which creep can't be measured. The modified power law equation then becomes:
where A, Q and m can all be explained by conventional mechanisms, and R is the gas constant. The creep increases with increasing applied stress, since the applied stress tends to drive the dislocation past the barrier, and make the dislocation get into a lower energy state after bypassing the obstacle, which means that the dislocation is inclined to pass the obstacle. In other words, part of the work required to overcome the energy barrier of passing an obstacle is provided by the applied stress and the remainder by thermal energy.
Nabarro–Herring creep
Nabarro–Herring creep is a form of diffusion creep, while dislocation glide creep does not involve atomic diffusion. Nabarro–Herring creep dominates at high temperatures and low stresses. As shown in the figure on the right, the lateral sides of the crystal are subjected to tensile stress and the horizontal sides to compressive stress. The atomic volume is altered by applied stress: it increases in regions under tension and decreases in regions under compression. So the activation energy for vacancy formation is changed by ±σΩ, where Ω is the atomic volume, the positive value is for compressive regions and negative value is for tensile regions. Since the fractional vacancy concentration is proportional to, where Qf is the vacancy-formation energy, the vacancy concentration is higher in tensile regions than in compressive regions, leading to a net flow of vacancies from the regions under tension to the regions under compression, and this is equivalent to a net atom diffusion in the opposite direction, which causes the creep deformation: the grain elongates in the tensile stress axis and contracts in the compressive stress axis.In Nabarro–Herring creep, k is related to the diffusion coefficient of atoms through the lattice, Q = Q, m = 1, and b = 2. Therefore, Nabarro–Herring creep has a weak stress dependence and a moderate grain size dependence, with the creep rate decreasing as the grain size is increased.
Nabarro–Herring creep is strongly temperature dependent. For lattice diffusion of atoms to occur in a material, neighboring lattice sites or interstitial sites in the crystal structure must be free. A given atom must also overcome the energy barrier to move from its current site to the nearby vacant site. The general form of the diffusion equation is
where D0 has a dependence on both the attempted jump frequency and the number of nearest neighbor sites and the probability of the sites being vacant. Thus there is a double dependence upon temperature. At higher temperatures the diffusivity increases due to the direct temperature dependence of the equation, the increase in vacancies through Schottky defect formation, and an increase in the average energy of atoms in the material. Nabarro–Herring creep dominates at very high temperatures relative to a material's melting temperature.