Saturday, September 1, 2007

Control of Residual Stresses

ASM Handbook, Volume 20: Materials Selection and Design U. Chandra, Concurrent Technologies Corporation
ALL THERMO-MECHANICAL manufacturing processes--such as forging, extrusion, casting, heat treatment, welding, coating, and machining--- create residual stresses in industrial products. There are situations when such stresses can be beneficial and are intentionally created, for example, compressive stresses on the outer surface of a component subjected to fatigue loads, autofrettage in gun barrels, and prestressed pressure vessels; even bolted connections and prestressed concrete can be included in this category. In many other situations, however, the presence of residual stress is detrimental to the integrity of the product under service conditions. Examples in this category include: tensile stresses on the outer surface of a component subjected to fatigue loads, tensile stresses on the inner surface of an austenitic stainless steel pipe caused by welding leading to intergranular stresscorrosion cracking in boiling water reactors, interlaminar stresses in coatings leading to their spallation, premature yielding or fracture (especially in brittle materials), and part distortion or dimensional instability. The presence of residual stresses in a part is also known to affect its machinability. For these reasons, mechanical and manufacturing engineers have long been interested in understanding the source of such stresses, their control, and relief (Ref 1-4). In the case of metallic products, the selection of material is generally dictated by functional requirements such as the ability of the product to withstand service loads, resistance to wear or corrosion, and so forth. It is rare that the magnitude and distribution of residual stresses is a matter of primary consideration while selecting the material to manufacture a metallic part. The issue facing the manufacturing engineer is to control the residual stresses in the product once the material (and often the manufacturing process) has already been selected. In the case of a composite or coated product, however, minimization of residual stresses is a prime consideration while selecting the constituent materials. This article primarily deals with metallic products. A logical way to control residual stresses in a product should consist of the following steps: 1. Understanding the fundamental sources of stress generation
2. Identifying the parameters that can cause residual stresses in a particular manufacturing process 3. Understanding the relative significance of each one of these parameters 4. Experimenting with the most significant process parameters until a suitable combination is obtained that results in the desired magnitude and distribution of residual stresses If the residual stresses in the product are still higher than acceptable, the only recourse left is the use of one of the various techniques of stress relief or the inducement of a su'ess pattern more favorable than the original. The fundamental sources of residual stresses in a product can best be understood with the help of the disciplines of solid mechanics, heat transfer, and metallurgy, as discussed in the section "Fundamental Sources of Residual Stresses" in this article. The identification of process parameters comes from an engineer's knowledge of and experience with a particular manufacturing process. Finally, to understand the relative significance of each process parameter and to arrive at their optimal combination one can use either of two approaches: trial and error on the shop floor combined with a suitable method of stress measurements, or computer simulation, especially one based on the finite element method. Both of these approaches have some advantages and limitations. In general, computer simulation offers a more economical and efficient means of performing a parametric study. It also helps in understanding the behavior of the product at various intermediate stages of its manufacture. For example, in case of forging, it is possible to monitor stresses during the entire duration of the die motion, as well as after the die removal. Computer simulation also helps in monitoring other phenomena of interest, such as the flow of material during forging. However, the trial-and-error approach offers only one opportunity to see the effect of changing a process parameter, for example, after the die removal. On the other hand, trial and error requires less investment in personnel training and development of a material properties database. Also, the use of physical modeling in a laboratory coupled with residual-stress measurements is still needed to verify the results of computer simulation until full confidence in the accuracy of simulation code and personnel skill is attained. Until recently, the trial-and-error approach has played a more prominent role in the control of residual stresses in industrial products, as compared to its simulation counterpart. However, in recent years, considerable progress has been made in computer simulation of several manufacturing processes, for example, casting, forging, quenching, and postweld heat treatment. In such processes, it is expected that computer simulation will soon be used routinely on the shop floor. Until then, a judicious combination of computer simulation and trial and error appears to be the most prudent approach to control the residual stresses. On the other hand, in the case of shot peening and some other processes, computer simulation is either not mature enough or is too uneconomical to be used as an alternative to trial and error, at least in the foreseeable future. It is important to note that, before attaining its final shape, a product often undergoes a series of primary and secondary operations; for example, it may involve forging as the primary operation and quenching, aging, and machining as the secondary operations. Each of these operations affects the state of residual stresses in the part. Therefore, in order to control the residual stresses in a finished product, it appears logical to apply the aforementioned techniques (either trial and error or computer simulation) for each operation. In some cases (e.g., forging followed by quenching), it may be argued that the final manufacturing operation is mainly responsible for the state of residual stresses in the part and, hence, the effort to control them should focus on the final operation. However, this argument does not apply if the sequence of quenching and machining is considered. Hence, it should not be used as a general rule. This article is an introduction to the subject of control of residual stresses. Its objectives are to: • Introduce the various fundamental sources of residual stresses common to most manufacturing processes • Explain the effect of material removal on residual stresses and distortions in a part
Provide a summary of commonly used techniques of measuring residual stresses • Provide a summary of the finite element method used for predicting residual stresses • Demonstrate the application of the above to a few selected manufacturing processes Because the number of manufacturing processes is too large, it is not possible to cover them all in a short article. Also, a listing of rules for control of residual stresses in various manufacturing processes is not attempted in this article, because an indiscriminate application of such roles without proper appreciation of the basic concepts could lead to adverse results. It is hoped that the article provides some insight to a manufacturing engineer into the cause of residual stresses in a product and assists in identifying key process parameters responsible for such stresses. The article is also expected to assist in making a choice between the trial-anderror and computer-simulation approaches (or a combination of the two) for the control of residual stresses. Fundamental Sources of Residual Stresses In manufacturing processes, residual stresses are caused by a combination of some or all of the following fundamental sources: • Inhomogeneous plastic deformation in different portions of the product due to mechanical loads or constraints • Inhomogeneous plastic deformation due to thermal loads • Volumetric changes and transformation plasticity during solid-state phase transformation
A mismatch in the coefficients of thermal expansion The mechanics related to these sources is explained in the remainder of this section. Also, an important concept related to the effect of material removal (e.g., a casting mold, a forging die, or the material removed during machining) on the magnitude and distribution of residual stresses in the workpiece is introduced. Mechanical Loads. Generation of residual stresses due to mechanical loads can be understood by consideration of the example shown in Fig. 1 (Ref 5). It consists of an assembly of three bars, each 254 mm (10 in.) long with a cross section of 25.4 mm (1 in.) square. The bars are spaced 25.4 mm (1 in.) apart, center to center. The two outer bars are made of the same material with an elastic modulus of 207 GPa (30 x 106 psi), yield strength of 207 MPa (30 ksi), and plastic modulus of 41 GPa (6 x 10 ° psi). The middle bar has a higher yield strength of 414 MPa (60 ksi), but the same elastic and plastic moduli as the two outer bars. The upper ends of the three bars are fixed and not allowed to move in any degree of freedom; their lower ends are tied to a rigid but a weightless block. Also, the assembly carded a load P in the center, as shown in Fig. 1. Now consider two different loading histories. In the In:st case, the load P is gradually increased from 0 to 400 kN (90 kips), and then brought back to zero. When P is 400 kN (90 kips), each bar shares 133 kN (30 kips) and the stress in none of them exceeds the yield strength. On unloading, the original zero stress state in each bar is restored, and no residual stresses are introduced. In the second case, P is increased from 0 to 534 kN (120 kips) and then brought back to zero. The entire history of stresses in the three bars is shown in Fig. l(b). When P exceeds 400 kN (90 kips), the two outer bars deform plastically and, be- cause of the reduced modulus, begin to share less load. The stress in the two outer bars follows the path ABCD, whereas that in the middle bar follows the path ABEF. It can be seen that when P is again zero (unloading), the stresses in the three bars do not go back to zero. Instead, the middle bar has a residual tensile stress of 78.8 MPa (11.4 ksi), and each of the two outer bars has a residual compressive stress of 39.4 MPa (5.7 ksi). Because there is no external load on the assembly, the residual stresses in the three bars are in selfequilibrium. A comparison of the two loading histories indicates that the presence of inhomogeneous plastic deformation in the three bars is responsible for the generation of residual stresses. Similarly, mechanical residual stresses occur in any component when the distribution of plastic deformation in the material is inhomogeneous, such as the surface deformation in shotpeening operation. Thermal Loads. A similar three-bar model explaining the generation of residual stresses due to inhomogeneous plastic deformation caused by thermal loads is discussed by Masubuchi (Ref 6, presumably adopted from Ref 7). In this model, three carbon-steel bars of equal length and crosssectional area are connected to two rigid blocks at their ends. The middle bar is heated to 593 °C (1100 °F) and then cooled to room temperature, while the two outer bars are kept at room temperature. Some of the details are not clearly explained in Ref 6, but the problem is very similar to the previous example. When the temperature in the middle bar is raised, the requirements of compatibility and equilibrium imply that a compressive stress be generated in the middle bar and tensile stresses in the two outer bars; the stress in each of the two outer bars being half of that in the middle bar. If the temperature in the middle bar is so high that its stress exceeds yield but in the two outer bars the stresses are still below yield, residual stresses will occur in the three bars when the temperature of the middle bar is brought back to room temperature (i.e., on unloading). Similarly, if the stresses in all three bars exceed yield but by different amounts, residual stresses will still occur when the temperature of the middle bar is brought back to room temperature. Indeed, this case is very similar to that of a cylinder immersed vertically in a quenchant where, during the initial stages of quenching, the temperature in the outer layer is much lower than that in the inner core. The three-bar model can be further utilized to explain the generation of residual stresses due to the mismatch in coefficients of thermal expansion. For example, suppose the two outer bars represent the layers of matrix in a composite lamina and the inner bar represents a layer of fibers. The coefficient of thermal expansion of the two outer bars is equal but, in general, different from that of the middle bar. It is assumed that the initial temperature of all the three bars is equal, which corresponds to a certain processing temperature much higher than room temperature. When the assembly is brought to room temperature, the requirements of compatibility and equilibrium will be satisfied if a system of forces (residual stresses) is established such that the sum Fig. 3 of the forces in the two outer bars is equal and opposite to that in the middle bar. In this case, the presence of unequal plastic deformation is not a prerequisite for the generation of residual stresses. This explains why, while selecting the constituent materials for a composite or for a coating, the designers try to minimize the mismatch between their coefficients of thermal expansion. Solid-State Transformation. In quenching, welding, and casting processes, many metals such as steels undergo one or more solid-state transformations. These transformations are accompanied by a release of latent heat, a change in volume, and a pseudoplasticity effect (transformarion plasticity). All of these affect the state of residual stresses in the part. The release of latent heat during solid-state transformation is similar to that during the liquid-to-solid transformation, albeit of a smaller amount. The change (increase) in volume occurs due to the difference in mass densities of the parent phase (e.g., austenite) and the decomposed phases (pearlite, ferrite, bainite, and martensite). In steels, the volumetric change due to phase transformation is in contrast to the normal contraction or shrinkage during cooling (Ref 8). A simple example of transformation plasticity is shown in Fig. 2, which is based on the results of a constrained dilatometry experiment (Ref 9). The figure shows that during cooling in the phase transformation regime, the presence of even a very low stress may result in residual plastic strains. Two widely accepted mechanisms for transformation plasticity were developed by Greenwood and Johnson (Ref 10) and Magee (Ref 11). According to the former, the difference in volume between two coexisting phases in the presence of an external load generates microscopic plasticity in the weaker phase. This leads to macroscopic plastic flow, even if the external load is insufficient to cause plasticity on its own. According to the Magee mechanism, if martensite transformation occurs under an external load, (a) martensitic plates are formed with a preferred orientation affecting the overall shape of the body.
Material Removal. A fact that is often overlooked in discussing residual stresses caused by various manufacturing processes is the effect of material removal on the state of stresses in the product. Consider, for example, that a casting mold must be finally broken and removed, or a forging die must be retracted. Likewise, in making a machined part some of the material has to be removed. All of these operations change the state of stress in the part. In order to fully understand this concept, three examples discussed in Ref 5 should be considered. The first example entails an assembly of two concentric springs of slightly different lengths, L i and L o, as shown in Fig. 3(a); the subscripts i and o refer to inner and outer springs, respectively. The bottom ends of the two springs are fixed. Then, the upper ends are tied to a rigid block that is free to move only in the vertical direction. The two springs adopt a compromise length, L, which is in between L i and L o, as shown in Fig. 3(b). As a result, the two springs develop equal and opposite forces: compressive in the longer inner spring and tensile in the outer shorter spring. The assembly of the two springs may be viewed as analogous to the assembly of a cast part and its mold or to the assembly of the forged part and the die, or to a machined part before some portion of it is removed. Then, the removal of the outer spring becomes analogous to removal of material during machining (Ref 5, 12), of the casting mold (Ref 13-16), or of the forging die (Ref 17). Two cases are considered. In the first case, the stresses in both springs are assumed to be within their elastic limits. When the outer spring is removed, the force acting on it is transferred to the inner spring in order to satisfy equilibrium and the inner spring returns to its original length. In the second case, it is assumed that the inner spring has undergone a certain amount of plastic deformation. When the outer spring is removed, the inner spring does not return to its original length, L i. In either case, because the two springs and, therefore, the forces, are concentric, the residual stress in the inner spring becomes zero when the outer spring is removed.
For the second example, reconsider the threebar model from the section "Mechanical Loads" in this article. After creating residual stresses in the three bars by loading and unloading the assembly, bar 3 is removed, by (for example) machining. As shown in Fig. 4(a) and (b), a redistribution of stresses in the remaining two bars takes place. The resultant stresses at the centroids of the two bars become -14.8 MPa (-2.14 ksi) in bar 1, and 14.8 MPa (2.14 ksi) in bar 2. Also, the assembly rotates (distorts) by an angle of 4.3 x 10 -3 radians. The third example in Ref 5 is of a thick-walled cylinder with an internal diameter of 101.6 mm (4 in.) and an outer diameter of 203.2 mm (8 in.) as shown in Fig. 5(a). Both ends of the cylinder are restrained axially, and the cylinder is subjected to an internal pressure. A 25.4 mm (1 in.) thick (along the axis) slice of the cylinder is analyzed by subdividing it into 10 equal finite elements (5.08 mm, or 0.2 in., thick each) in the radial direction (Fig. 5b). The residual stresses are created by increasing the pressure from zero to 345 MPa (50 ksi), and then back to zero. The elements 1 and 2 are removed successively. The variation of the three stress components along the radius is shown in Fig. 6, before material removal (i.e., the residual stresses) and after removing the two layers. It may be noted that in an overall sense, the level of residual stresses goes down as the material is removed. However, this is not necessarily true in a local sense. Consider, for example, the circumferential stress at the centroids of elements 3 and 4 in Fig. 6(b); it increases as the material is removed. Important conclusions from the three examples discussed above can be summarized as follows: • When the material removal is symmetric with respect to the stress distribution (Fig. 3), the residual stresses in the remainder of the assembly or part are very small or even zero. • When the material removal is not symmetric with respect to the stress distribution (Fig. 4, 6), the residual stresses in the remainder of the assembly or part are not necessarily small. • Material removal may result in an increase in stresses at some locations of the assembly or the part (Fig. 6). Computer Prediction of Residual Stresses In recent years, the finite element method has become the preeminent method for computer prediction of residual stresses caused by various manufacturing processes. A transient, nonlinear, thermomechanical analysis software is generally employed for that purpose. Some of the mathematics that form the basis of such software is common for all manufacturing processes. Such common mathematics is summarized by this section. However, because every process is unique, some mathematical requirements are, in turn, dependent on the process. Also, for the simulation of certain processes a sequential thermomechani-
cal analysis is adequate, whereas for others a coupled analysis may be preferred or even essential. Such subtleties are pointed out later when individual processes are discussed. Ignoring convection, the following conduction heat-transfer equation is solved with appropriate initial and boundary conditions: • aT v . (kw3 + Q~ =pcp aTt (Eq t)
where Tis the temperature at an arbitrary location in the workpiece at time t, k is the thermal conductivity of the material, Qc is the rate of heat generated per unit volume p is the density (7_ is the specific heat • ' . . ' l / . ' and V is the differential operator; all material properties are assumed to vary with temperature. The term Qc accounts for the release of latent heat during liquid-to-solid transformation in casting and welding processes or during solid-state phase transformation in quenching, welding, or casting processes. It also accounts for the heat of plastic deformation in forging and other bulk deformation processes. The initial and boundary conditions are process dependent. Details of converting Eq 1 into its finite element form and of numerical solution are available in a number of technical papers and textbooks and are not repeated here. For a general treatment of the subject, the reader is referred to Ref 18 to 21. The transient temperatures computed above are used as loading for the subsequent transient stress/displacement analysis. Using the incremental theory, the total strain increment {Ae} at time t can be divided into various components (Ref 22-26): {Ae} = {Ae e} + {AE t} + {Ae p} + {Ae or} + {Ae v} + {AE tr} (Eq 2) where superscripts e, t, p, cr, v, and tr refer to elastic, thermal, plastic, creep, volumetric change, and transformation plasticity components, respectively. The first three strain terms are needed in the simulation
simulation of every manufacturing process discussed here, whereas the use of the other three terms is dependent on the process and are pointed out as appropriate. Also, mathematical details for the first four strain terms are discussed in most standard references (Ref 22, 23), whereas the details for the last two terms are discussed often in the context of the simulation of quenching and welding processes (Ref 24-26). In forging and other large deformation processes, the term Qc in Eq 1 represents the heat of plastic deformation and leads to a coupling between Eq 1 and 2. At present, no single computer code is capable of predicting residual stresses caused by all manufacturing processes. However, several general- purpose finite element codes are capable of predicting these stresses to a reasonable degree of accuracy for at least some of the manufacturing processes (Ref27-29). In addition, some of these codes permit customized enhancements leading to more reliable results for a specific process. Before attempting to predict residual stresses due to a manufacturing process, it is advisable to compare the capabilities of two or three leading codes and use the one most suited for the simulation of the process in consideration. Examples of such comparisons are given in Ref 12 and 13 for forging, quenching, and casting processes. It must be noted that, due to continuous enhancement in these codes, it is always advisable to compare the capabilities of their latest versions. Measurement of Residual Stresses It is generally not possible to measure residual stresses in a product during its manufacture; instead, they are measured after the manufacturing process is complete• Smith et al. (Ref 30) have divided the residual stress measurement methods into two broad categories: mechanical and physical. The mechanical category includes the stressrelaxation methods of layer removal, cutting,
hole drilling, and trepanning, whereas the physical category includes x-ray diffraction (XRD), neutron diffraction, acoustic, and magnetic. The layer-removal technique as originally proposed by Mesnager and Sachs (Ref4) is only applicable to simple geometries such as a cylinder with no stress variation along its axis or circumference, or to a plate with no variation along its length or width. Thus, whereas it could be used to measure quench-induced residual stresses in a cylinder or a plate, it is not suitable for measuring complex stress patterns such as those caused by welding. The layer removal and cutting techniques, however, have been applied to pipe welds in combination with conventional strain gages and XRD measurements. The layer-removal technique is also used to measure residual stresses in coatings. Hole-drilling and trepanning techniques can be used in situations where the stress variation is nonuniform, but they are generally restricted to stress levels of less than one-third of the material yield strength. Also, these two techniques can be unreliable in areas of steep stress gradients and require extreme care while drilling a hole or ring in terms of its alignment as well as the heat and stress generation during drilling (Ref 31). For such reasons, and others, these two techniques have found little application in the measurement of weld-induced residual stresses. Of the methods in the physical category, XRD is probably the most widely used method, the neutron diffraction method being relatively new. These two methods measure changes in the dimensions of the lattice of the crystals, and from these measurements the components of strains and stress are computed. The XRD technique has undergone many improvements in recent years. With the development of small portable x-ray diffractometers, the technique can be used for on-site measurement of residual stresses. It should be noted, however, that this technique is capable of measuring strains in only a shallow layer (approximately 0.0127 ram, or 0.0005 in., thick) at the specimen surface. To measure subsurface residual stresses in a workpiece, thin layers of materials are successively removed and XRD measurements are made at each exposed layer. For reasons discussed in the section "Material Removal" in this article, the measurements at an inner layer should be corrected to account for the material removed in all the previous layers. Reference 32 gives analytical expressions for such corrections in cases of simple geometries and stress distributions. For more complex cases, it still remains difficult to determine subsurface residual stresses accurately. In contrast to the x-rays, neutrons can penetrate deeper into the metals. For example, in iron the relative depth of penetration at the 50% absorption thickness is about 2000 times greater for neutrons than for x-rays. Only a few materials, such as cadmium and boron, absorb neutrons strongly. However, to gain the advantage of greater penetration of neutrons requires the component to be transported to a high flux neutron source (Ref 30), which limits the use of the technique. Residual Stresses Caused by Various Manufacturing Processes Casting. In the past, little attention has been paid to the control of residual stresses in casting; much of the interest was focused on the prediction and control of porosity, misruns, and segregation. A review of the transactions of the American Foundrymen's Society or of earlier textbooks on casting (e.g., Ref 33) reveals practically no information on the subject; even the ASM Handbook on casting (Ref 34) provides little insight. In a recent book, Campbell (Ref 35) has included a brief discussion of residual stresses summarizing the work done by Dodd (Ref 36) with simple sand-mold castings. Dodd studied the effect of two process parameters: mold strength, by changing water content of sand or by ramming to different levels, and casting temperature. The conclusions of these costly experiments could have been more economically and easily arrived at by using the basic concepts discussed in the section "Fundamental Sources of Residual Stresses" and further amplified in the following paragraphs. When a casting is still in its mold, the stresses are caused by a combination of the mechanical constraints imposed by the mold, thermal gradients, and solid-state phase transformation. Also, creep at elevated temperature affects these stresses. Finally, when the casting is taken out of its mold, it experiences springback that modifies the residual stresses. As discussed in Ref 13 to 16, the computer prediction of residual stresses in castings requires a software that is capable of performing coupled transient nonlinear thermomechanical analysis (see the section "Computer Prediction of Residual Stresses" in this article). In addition, it should be able to account for the following: • Release of latent heat during liquid-to-solid transformation, that is, in the mushy region • Mechanical behavior of the cast metal in the mushy region • Transfer of heat and forces at the mold-metal interface • Creep at elevated temperatures under condition of varying stress • Enclosure radiation at the mold surface to model the investment-casting process • Mold withdrawal to model directional solidification • Mold (material) removal The author and his coworkers have recently modified a commercial finite element code and have analyzed simple sand-mold castings (Ref 15, 16). Computer simulation of these castings indicates that: (1) for an accurate prediction of transient and residual stresses, consideration of creep is important; creep is also found to make the stress distribution more uniform; and (2) just prior to mold removal the stresses in the casting can be extremely high, but after the mold removal they become very small (owing to the springback discussed in the section "Material Removal") except in the areas of stress concentration. The residual stresses after the mold removal will not necessarily be small if the casting is complex and the mold removal is asymmetric with respect to the stress distribution. Also, small variations in mold rigidity are not found to have any noticeable effect on residual stresses, which confLrrns the observations based on trial and error using greensand molds with various water contents (Ref 35). Although very little work is published thus far on the subject of control of residual stresses in castings, finite element simulation methodology is now sufficiently advanced to enable the study of the effect of various process and design parameters on the residual stresses in castings, for example, superheat, stiffness and design of the mold, design of the feeding system and risers, and the design of the part itself. Also, residual stresses caused by different casting practices such as sand-mold, permanent-mold, investment casting, and so forth, can be determined. As the manufacturers and end-users of cast products become more aware of the status and benefits of the computer- simulation methodology, it can be expected
to play a very important role in controlling residual stresses in complex industrial castings. At present, the biggest limiting factor in the use of simulation is the lack of thermophysical and mechanical properties data for the cast metal and the mold materials. Forging. As with the casting process, little attention has been paid in the past to the control of residual stresses caused by forging; most of the interest was in predicting the filling and the direction of material flow. Now, due to recent advances in computer-simulation techniques, it is possible to predict and control the residual stresses in forged pans. Large plastic flow of the workpiece material is inherent in the forging process. The material flow is influenced by a number of factors including the die shape and material, forging temperature, die speed, and lubrication at the die/workpiece interface. Therefore, finite element simulation software used to predict and control residual stresses in the part should be capable of accounting for these factors. Because a significant amount of energy is dissipated during forging in the form of heat due to plastic deformation, a coupled thermomechanical analysis becomes necessary especially for nonlsothermal forging. Other factors contributing to the complexity of the finite element simulation of this class ofproblems are: temperature-dependent thermal and mechanical properties of the materials (especially for a nonisothermal forging); the choice of solution algorithm and remeshing due to large plastic deformation in the workpiece; and mathematical treatment of the die/workpiece interface that includes heat transfer, lubrication, and contact. The last two terms in Eq 2 need not be considered in the simulation of the forging process. Finite element simulation of the forging process with simple geometries and of a two-dimensional idealization of the thread-rolling process (Ref 17) showed that, although the stresses in the workpiece are high during the deformation stage, the stresses after retraction of the die (residual stresses) are no longer high except in the regions of stress concentration. Again, similar to the simulation of the casting processes, it is premature to generalize this conclusion but it is clear that the technique of computer simulation of forging and many other bulk deformation processes has advanced to a stage where it can assist in controlling the residual stresses in the part by performing a detailed parametric study with much less investment of time and capital than trial and error on the shop floor. Quenching involves heating of the workpiece to the heat treatment temperature followed by rapid cooling in a quenchant (e.g., air, water, oil, or salt bath) in order to impart the desired metallurgical and mechanical properties. The choice of a quench medium is the key element; it should be such that it removes the heat fast enough to produce the desired microstructure, but not too fast to cause transient and residual stresses of excessive magnitude or of an adverse nature (e.g., tensile instead of compressive). The heat removal characteristic of a quenchant is known to be affected by a number of factors including the size, shape, orientation of the workpiece (even for simple shapes such as plates and cylinders, the heat removal is different at the bottom, top, and side surfaces); the use of trays and fixtures to hold the workpiece in the quenchant; composition of the quenchant; size of the pool and its stirring, and so forth (Ref 37-39). Additional difficulties arise when, due to economic reasons, quenching is performed in a batch process. In the past, using trial and error, shop-floor personnel have come up with some interesting strategies to control the residual stresses (and warpage), for example, air delay or an intentional delay while transporting the workpiece from the heating furnace to the quenchant, and time quenching or performing the quenching operation in two steps. In the first step, the part is quenched in a medium such as a salt bath until the part has cooled below the nose of time-temperature transformation curve, followed by quenching in second medium such as air to slow the cooling rat& Obviously, perfecting the quenching operation by trial and error can be an extremely time-consuming task. At first glance, computer simulation of the quenching process may appear to be simple. It involves an uncoupled transient nonlinear small deformation thermomechanical analysis (as outlined in the section "Computer Prediction of Residual Stresses" in this article), with due consideration to solid-state transformation effects (Ref 9, 24, 25); creep is generally ignored. However, the major difficulty lies (for reasons discussed in the preceding paragraph) in a lack of knowledge of the heat removal characteristic of various quenchants, which is mathematically represented as the convective heat transfer coefficient at the outer boundary of the workpiece. Other difficulties arise due to the lack of thermophysical and mechanical properties of the workpiece material at elevated temperatures. Still, at least in the United States, major aircraft engine manufacturers and their forging vendors have been using computer simulation to control quench-related cracking and residual stresses for some time. One such example involving a turbine disk is discussed in Ref 40. The reported work was performed without the benefit of sophisticated simulation software that could account for solid-state transformation effects. For proprietary reasons, few such cases are published in the open literature. Machining. Many complex parts in aerospace and other key industries are made by machining forgings, castings, bars, or plates to their net shapes. The presence of residual stresses in the workpiece affects its machinability and, on the other hand, the machining process also creates residual stresses and undesired distortions in the part and alters the already existing stress state. In order to minimize or eliminate these adverse effects, machine-shop personnel often experiment with a number of process parameters, for example, depth of cut, speed of the cutting tool, and coolant. For single-point turning, they frequently flip the workpiece in order to balance the distortions and stresses evenly on the two sides. This trial and error is frequently combined with statistical process control. A serious problem associated with machining and residual stresses is often manifested in the form of part distortion. For example, consider the example in Table 1 (Ref 12). The table shows the results of a dimensional check on 30 samples of an aircraft engine part that was made by machining heat treated forgings procured from three different vendors (10 samples each). The location at which the dimensional check was performed is identified on the figure included in the table. It was found that: (1) for all forgings from any one vendor, the drop was almost identical; (2) the drop in forgings from vendor B was within the specifications, but not so in the case of the other two vendors; and (3) the drop in forgings from vendors A and C was on the two opposite sides of that from vendor B. It was recognized that all heat treated forgings contained residual stresses. When these forgings were machined to net shapes, distortions occurred for two reasons: the release of residual stresses from the removed portion of the workpiece and the machining process itself. The former can be easily modeled using the finite element method if the magnitude of residual stresses in the forgings prior to machining is known (Ref 5). However, to this author's
knowledge, no serious attempt has so far been made to predict residual stresses in a workpiece due to the machining process itself. If an attempt of this type is to provide reliable results, it must take into account such factors as: depth of cut, speed of the cutting tool, interaction between the tool and the workpiece (heat and force), coolant, and clamping/unclamping of the workpiece. It must also recognize the fact that the location of contact between the tool and the workpiece moves as the machining process progresses. If such technology could be developed, it would become possible to predict and control the overall distortions and residual stresses in a part after machining, thereby reducing scrap. Welding. The residual stress distribution in welded joints depends on a number of process and design parameters such as the heat input, speed of the welding arc, preheat, thickness of the welded part, groove geometry, and weld schedule. Welding engineers have long used trial and error to obtain a suitable combination of these parameters in order to control the residual stresses. The role of computer simulation in the prediction of residual stresses in weldments is the subject of a recent review (Ref 14). Major elements of computer simulation of the process are: • Mathematical representation of the heat input from the welding source • A transient thermal analysis • A transient stress/displacement analysis; the flow of molten metal and thermal convection in the weld pool are generally ignored Following Rosenthal (Ref 41), a semisteady state approach is often used, although some attempts at full three-dimensional analysis have also been made. As mentioned earlier, it is now possible to account for volumetric change and transformation plasticity effects. Because of the short time periods involved, creep is ignored. In the case of a singlepass weld or a weld with few passes (e.g., four or five), it is now possible to predict residual stresses with reasonable accuracy. But, as the number of passes increases (e.g., 20 or 30), it becomes computationally intractable to model each pass. The scheme of lumping several passes into one layer has been employed with less than satisfactory results. In addition to excessive computation time, other major difficulties with the simulation of a mulfipass weld ale: the numerical errors tend to accumulate with each pass, and the changes in metallurgical and mechanical properties of material in previously deposited layers during deposition of a subsequent layer are difficult to quantify and to account for in the finite element analysis. The technique of lumping several layers together aggravates these problems. Between the mid 1970s and early 1980s, the Electric Power Research Institute (EPR1) in the United States sponsored a program to systematically study the effects of various process and geometric parameters such as the heat input, welding method (gas tungsten arc welding, submerged arc welding, laser, and plasma), speed of the welding arc, diameter and thickness of the pipe, and groove geometry, on residual stresses in pipe welds (Ref42-51). In addition, various thermal processes such as heat-sink welding, backlay welding, and induction heat treatment were investigated to verify if the residual stresses on the inner surface of the pipe could be changed from tensile to compressive to avoid intergranular Stress-corrosion cracking. Both experimental and finite element methods were used in the study. The results of this effort are summarized in Ref 52. A very interesting effort related to in-process control and reduction of residual stresses and distortions in weldments is being pursued (Ref 53, 54). The effort aims at moving beyond mere analysis of residual stresses and distortions to aggressively controlling and reducing them. To accomplish this objective, the effort is subdivided into the development of the following three primary capabilities: prediction, sensing, and control. For prediction purposes, a series of computer programs have been developed, include simple but fast one-dimensional programs that analyze only the most important stress component, that is, the one parallel to the weld line. Sensing capability refers to a set of devices including a laser interferometer to measure minute amounts of distortions, a laser vision system to measure large amounts of distortions, and a mechanical system to measure radi of curvature. Finally, to control the residual stresses, various techniques including changes in heating pattern and application of additional forces have been attempted. References 53 and 54 provide further examples of the application of this methodology in reduction of residual stresses in weldments in high-strength steels and girth-welded pipes. Coating. Coatings are being used extensively in aerospace, marine, automobile, biomedical, electronics, and other industries. For example, in modem jet aircraft engines, approximately 75% of all components are coated. Some of the reasons for the application of coatings are: thermal bartier, wear resistance, corrosion resistance, oxidation protection, electrical resistance, and repair or dimensional restoration of worn parts. A variety of methods are used for the deposition of coatings on a substrate; the following discussion is limited primarily to the thermal spray process. The prediction of residual stresses in a coating/ substrate system is in its infancy. These stresses result from the difference in the coefficient of thermal expansion of the coating and substrate materials and from plastic deformation of the substrate material. The limited number of numerical studies conducted thus far have been related to small button-type specimens where the coating material was assumed to be fully molten and deposited instantaneously. These efforts have ignored several important factors, for example: • The presence of partially molten particles in the spray • A nonuniform deposition of coating material normal to the axis of the plasma jet • A liquid-to-solid and solid-state transformation • Imperfect bond between the coating and the substrate • The relative motion between the spray and the substrate Also, because a layer of coating consists of several successive passes, the effect of any new pass on its adjacent previously deposited pass in terms of partial remelting, additional material buildup, solute diffusion, and redistribution of residual stresses could be important and should be accounted for. If more than one layer is involved, for example, in functionally graded coatings, modeling the effect of a whole new layer of material on the previously deposited layer would be computationally prohibitive. Also, due to the morphology of the coating material on deposition, its thermal and mechanical properties are extremely difficult to measure and, thus, are generally unavailable for simulation purposes. Due to such reasons, end-users of coated products still rely on the methods of trial and error and statistical process control for the selection of an optimal combination of process parameters in order to control the residual stresses in coated parts (Ref 55). Stress-Relief Methods The basic premise of a stress-relief method is to produce rearrangement of atoms or molecules from their momentary equilibrium position (higher residual stress state) to more stable positions associated with lower potential energy or stress state. These methods can be classified into three broad categories: thermal, mechanical, and chemical (Ref 4, p 134). The following concern the methods in the first two categories. Thermal stress-relief methods include annealing, aging, reheat treatment (e.g., postweld heat treatment), and others. In general, a stress-relief operation involves heating the part to a certain temperature, holding at the elevated temperature for a specified length of time, followed by cooling to room temperature. Primary reduction in residual stresses takes place during the holding period due to creep and relaxation. Thus, computer simulation of a thermal stress-relief method generally entails a thermal-elastic-plastic-creep analysis of the part. A simple, one-dimensional computer analysis of residual stresses in thin plates along with experimental verification is discussed by Agapakis and Masubuchi (Ref 56). More sophisticated thermal-elastic-plastic-creep simulations of the annealing of single pass and multipass girth-butt welds in pipes are presented in Ref57 and 58. A number of subcategoties of mechanical stress-relief methods are listed in Ref 4. Of these, the methods in the static-stressing subcategory such as stretching, upsetting, bending and straightening, and autofrettage are common, and these should not pose much difficulty in simulation by the finite element method. Similarly, in the mechanical surface treatment subcategory, it should be possible to model the surface-rolling method. However, within the same subcategory,
method) is likely to be difficult to simulate; and to this author's knowledge, no realistic attempt has yet been made to do so. The obvious reason is that, whereas it should be possible to model a single impact, modeling multiple impacts will be difficult,just as it is for modeling multipass welding. In recent years, the method of vibratory stress relief (especially in the subresonant region) has received considerable attention (Ref 59, 60). The basic premise of this method is that the presence of residual stresses in a part changes (increases) its natural resonant frequency. When the part is subjected to vibrations below its new frequency, the metal absorbs energy. During this process, the stresses redistribute gradually and the resonant frequency shifts back to the point corresponding to a residual stress-free (or almost free) state. The process does not change the metallurgical or mechanical properties of the material. The technique has been found successful in relieving residual stresses induced by thermal processes such as welding and casting, but not those induced by cold working. It has also been applied to reduce residual stresses in parts prior to machining in order to minimize distortions. It has been found particularly beneficial in low- and medium-carbon steels, stainless steels, and aluminum alloys, but not in copper alloys. In view of the fact that the technique is much simpler, quicker, and more inexpensive than the thermal-relief methods, it merits further study. ACKNOWLEDGMENT The author would like to thank H.A. Kuhn for providing many valuable technical suggestions.

1 comment:

Yang Di Sayangi said...

Great write-up

Keep it up

Charlie

Re: [MW:34832] Inquiry about Single Bevel with Back Grinding

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