Materials Transactions, Vol. 46, No. 9 (2005) pp. 1951 to 1956 #2005 The Japan Institute of Metals OVERVIEW An Analysis of Flow Mechanisms in High Temperature Creep and Superplasticity Terence G. Langdon* Departments of Aerospace & Mechanical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089-1453, U.S.A. The flow of crystalline solids at elevated temperatures is dependent upon creep mechanisms associated with the movement of dislocations, the relative displacements of adjacent grains and the stress-directed flow of vacancies. It is convenient to express the steady-state creep rate in terms of the dependences of these various creep mechanisms on the applied stress, the testing temperature and the grain size of the material. In practice, however, there are similarities in some of the predicted dependences for different creep processes and this may lead to experimental difficulties in unambiguously identifying the rate-controlling creep mechanism. The difficulties in identifying the creep mechanism become especially significant at low stresses. This paper reviews the characteristics of the various flow processes occurring in simple metallic systems such as pure metals and metallic alloys and describes procedures that may be adopted to provide an unambiguous identification of the rate- controlling flow mechanism. (Received June 17, 2005; Accepted July 1, 2005; Published September 15, 2005) Keywords: creep mechanisms, diffusion creep, grain boundary sliding, Harper–Dorn creep, superplasticity 1. Introduction similar values. This paper addresses this problem by examining the possibility of seeking additional experimental Creep flow refers to the plastic deformation occurring over information that may help in achieving an unambiguous a period of time when a crystalline solid is subjected to a load identification of the rate-controlling process. which is not sufficient to cause immediate fracture. Creep is a To place this paper in perspective, the following section diffusion-controlled process and therefore it becomes of provides a brief review of the potential mechanisms occur- major importance at elevated temperatures, typically at ring in high temperature creep, sections 3 and 4 examine the temperatures at and above 0:5 Tm where Tm is the absolute mechanisms occurring at high and low stresses, respectively, melting temperature of the material. and section 5 describes the additional information that is In practice, the rate of creep depends primarily upon the needed to achieve unambiguous identifications. For simplic- testing temperature through the diffusion coefficient and ity, attention is restricted to simple metallic systems such as upon the magnitude of the applied stress. The microstructural pure metals and solid solution alloys. More complex systems, features of the material are also important, especially the such as composite materials, may experience additional creep grain size since the creep rate often increases when the grain mechanisms related to their microstructural characteristics size is reduced. The various flow mechanisms occurring but these mechanisms are beyond the scope of this brief during creep are usually defined in terms of the rate of flow report. under steady-state conditions where the strain increases uniformly as a function of time. For these conditions, it is 2. The Flow Mechanisms Occurring in High Temper- convenient to express the steady-state creep rate, "_,bya ature Creep relationship of the form: ADGb b p n The flow of a crystalline material is dependent upon the "_ ¼ ð1Þ presence of defects in the material, where these defects may kT d G be localized at points (vacancies), lines (dislocations) or where D is the diffusion coefficient (¼ Do expðQ=RTÞ planes (grain boundaries). In broad terms, creep flow is due to where Do is a frequency factor, Q is the appropriate the movement of dislocations within the crystalline matrix, to activation energy for the diffusive process and R is the gas the relative displacements of adjacent grains in the process of constant), G is the value of the shear modulus at the testing grain boundary sliding and to the flow of vacancies under the temperature, b is the Burgers vector of the material, k is action of the applied stress. Each of these flow processes is Boltzmann’s constant, p and n are constants defined as the considered in turn in the following sections and each flow inverse grain size exponent and the stress exponent, mechanism leads to specific predictions for the values of Q, p respectively, and A is a dimensionless constant. and n. An important requirement in all creep testing is to It follows from eq. (1) that the steady-state creep rate determine the rate-controlling creep mechanism under any varies with the applied stress raised to a power of n. selected testing conditions. This evaluation requires an Therefore, a standard procedure in creep experiments is to experimental determination of the values of Q, p and n and plot, in a double-logarithmic form, the steady-state strain rate a comparison between these values and the various theoret- against the applied stress. An example of this approach is ical models available in the creep literature. In practice, shown schematically in Fig. 1. Over a wide range of high and however, this comparison may be difficult, if not impossible, intermediate stresses, the creep rate varies with stress raised if several different theoretical models predict reasonably to a reasonably high power of 3{5 and in this region the flow is dominated by the intragranular movement of *Corresponding author, E-mail: [email protected] dislocations: this behavior is generally termed power-law 1952 T. G. Langdon Fig. 2 The principle of intragranular dislocation glide and climb in high temperature creep.1) power-law creep. An example is shown in Fig. 2 where dislocation loops are emitted and expand outwards from an array of dislocation sources, such as Frank–Read sources, located on different slip planes.1) Since there is an interaction between the stress fields of the leading dislocations on different but parallel slip planes, the leading screw disloca- tions on these different planes will have opposite signs and they readily cross-slip and annihilate. By contrast, the leading edge dislocations are blocked by these mutual interactions so that the edge dislocations pile up on each separate slip plane. Ultimately, the back stresses exerted on the sources by these pile-ups are relieved when the leading edge dislocations Fig. 1 Schematic illustration of the steady-state strain rate, "_, versus the applied stress, , for a typical polycrystalline metal. The plot shows the climb together and annihilate each other. It follows, there- occurrence of dislocation creep over a range of intermediate stresses, fore, that the annihilation process permits the emission of an power-law breakdown (PLB) at very high stresses and the occurrence of additional loop from the source and in this way a regenerative several different creep mechanisms at low stresses: the question mark process is created in which the rate of plastic flow is signifies the difficulties in unambiguously identifying the rate-controlling determined by the rate of climb. It is apparent also that this process at these low stresses. process is capable of producing very large creep strains. An early model of creep controlled by dislocation climb creep. At even higher stresses, the creep rate varies incorporated the assumption that the dislocations can exponentially with stress where this behavior marks a efficiently absorb and emit vacancies. For this model, it transition from diffusion-controlled flow at the lower stresses was shown that the steady-state creep rate is given by eq. (1) to a thermally-activated region analogous to flow at low with the values of n ¼ 4:5, Q ¼ Ql where Ql is the activation temperatures. This transition is generally termed the power- energy for self-diffusion and p ¼ 0 since the process occurs law breakdown and it is marked as PLB in Fig. 1. There are intragranularly.2) It has been shown through detailed analysis several possible creep mechanisms occurring at low stresses, of a wide range of data for f.c.c. metals that the precise value including the stress-directed flow of vacancies in diffusion of n may be higher than 4.5 in climb-controlled creep because creep, grain boundary sliding (GBS) and a dislocation of a dependence upon the stacking-fault energy of the mechanism known as Harper–Dorn creep. As indicated by material.3) the question mark in Fig. 1, these various mechanisms tend to For pure metals, the dislocations glide outwards very have fairly similar dependences on stress, temperature and rapidly from the dislocation sources so that climb is the rate- grain size and accordingly it is often not easy to make an controlling step. However, in some solid solution alloys there unambiguous identification of the precise rate-controlling may be a preferential segregation of solute atoms around the mechanism in this creep region. moving dislocations in the form of impurity or Cottrell The following section describes the behavior in the atmospheres4) and the rate of glide may then become slower intermediate and high stress region where dislocations than the rate of climb. Under these conditions, creep is control the creep process and the following section describes controlled by glide in the form of a viscous drag process and the characteristics of flow in the low stress region where the it was shown that the steady-state creep rate is given by behavior becomes more ambiguous.