Residual-stress

It is the stress existing in a body at rest, in equilibrium, at uniform temperature, and not subjected to external forces. Oft en caused by the stresses remaining in a plastic part as a result of thermal and/or mechanical treatment in fabricating parts. Usually they are not a problem in the finished product. However, with excess stresses, the product could be damaged quickly or after in service from a short to long time depending on amount of stress and the environmental conditions around the product. 

For certain products long time dynamic (creep, fatigue, impact, etc.) mechanical load performances in different environments are required. Dynamic loading in the present context is taken to include deformation rates above those achieved on the standard laboratory-testing machine (commonly designated as static or quasi-static just reviewed). These slower tests may encounter minimal time-dependent effects, such as creep and stress-relaxation, and therefore are in a sense dynamic. Thus the terms static and dynamic can be overlapping. 

A one-dimensional model of stress buildup in silicon devices over a temperature range is given by the following equation 

Since the coefficients of thermal expansion below the for most adhesives range from 25-100 ppm/°C and are greater than the CTEs of the device or substrate materials, stresses in bonded parts are compressive on the die and substrate and tensile on the adhesive. 

Another equation for maximum stress in rectangular devices addresses differences in both coefficients of expansion and moduli as follows  

L is length of the die X is the bondline thickness Tg is the cure temperature T is the application temperature 

In summary, the stress (typically at the edge ofthe die) increases with die size, modulus of the adhesive, temperature, difference in expansion coefficients, and increasing bondline thickness. 

---

Residual stresses in the formation, resulting from regional tectonic forces may cause the borehole to collapse or deform resulting in stuck pipe. Prevention sometimes high mud weights may help delay deformation of the bore hole. 

Tensor Field Tomography for Residual Stress Measurement in Class Articles. 

Using the equilibrium equations of the elasticity theory enables one to determine the stress tensor component (Tjj normal to the plane of translumination. The other stress components can be determined using additional measurements or additional information. We assume that there exists a temperature field T, the so-called fictitious temperature, which causes a stress field, equal to the residual stress pattern. In this paper we formulate the boundary-value problem for determining all components of the residual stresses from the results of the translumination of the specimen in a system of parallel planes. Theory of the fictitious temperature has been successfully used in the case of plane strain [2]. The aim of this paper is to show how this method can be applied in the general case. 

Many authors have shown that residual stresses in glass articles can be formally considered as the thermal stresses due to a certain fictitious temperature field. In the general case... 

Theory of the fictitious temperature field allows us to analyze the problems of residual stresses in glass using the mathematical apparatus of thermoelasticity. In this part we formulate the boundary-value problem for determining the internal stresses. We will Lheretore start from the Duhamel-Neuinan relations... 

Using flaw visuahzation system data the strength and fracture mechanics estimations are carried out in accordance with defect assessment regulatory procedure M-02-91 [5]. Recently, the additions had been included in the procedure, concerning interpretation of expert flaw visualization sysf em data, computer modelling, residual stresses, in-site properties of metal, methods of fracture analysis. 

In order to describe inherited stress state of weldment the finite element modelling results are used. A series of finite element calculations were conducted to model step-by-step residual stresses as well as its redistribution due to heat treatment and operation [3]. The solutions for the reference weldment geometries are collected in the data base. If necessary (some variants of repair) the modelling is executed for this specific case. 

Arzhaev A.I., Bougaenko S.E., Smirnov Yu.I., Aladinsky V V, Makhanev V.O., Saburov Yu. Residual stress modelling and analysis for INPP primary circuit pipeline welds. Transactions of the 14th Int. Conf. on Structural Mechanics in Reactor Technology (SMiRT 14), Lyon, 1997, Vol. 1, Div, B, pp. 345-352. 

FI43S7 Variation of residual stresses in aged components Dr R.H. Leggett The Welding Instrtute... 

Weldments subjected to corrosive attack over a period of time may crack adjacent to the weld seams if the residual stresses are not removed. Gas—tungsten arc welding and gas—metal arc welding ate recommended for joining magnesium, the former for thinner materials and the latter for thicker materials. Maintaining a protective atmosphere is a critical issue in welding these alloys. 

Crack Reflection. Crack deflection can result when particles transform ahead of a propagating crack. The crack can be deflected by the locali2ed residual stress field which develops as a result of phase transformation. The force is effectively reduced on the deflected portion of the propagating crack resulting in toughening of the part. 

Thermoformability is a property required by the many sheet materials used in the thermoforming industry. These properties are unique for the specific forming methods used, and are best determined by actual thermoforming tests on smaU-scale equipment. The softening or drape temperature of the material, residual stress in the sheet from its manufacture, and its melt strength and viscosity are important parameters relating to this use. 

Equation 7 predicts the correct yield pressure only if the material is isotropic, the cylinder free from residual stress prior to the appHcation of pressure, and sufftcientiy long, eg, more than five diameters, for there to be no end effects. 

The residual shear stress distribution in the assembled cylinders, prior to the appHcation of internal pressure, may be calculated, from pressure P, generated across the interface. The resulting shear stress distribution in the compound cylinder, when subjected to an internal pressure may be calculated from the sum of the residual stress distribution and that which would have been generated elastically in a simple cylinder of the same overall radius ratio as that of the compound cylinder. 

Provided the design is such that it can be represented by coordinates which fall within the unshaded area, then the residual stress will not exceed the yield strength of the material. When the cylinder is built up of n components of the same material, it can be shown (35,36) that the interference per unit radius required for all cylinder mating operations is given by... 

Relaxation of the residual stresses induced by autofrettage at 720 MPa (104,400 psi) in reactor tubes k = 2.4), of AISI 4333 M6 at a uniform temperature of 300°C has been studied and it was concluded, on the basis of creep tests for 10,000 h, that after 5.7 years 60% of the original stress would remain (161). 

Fig. 7. Comparison of relaxation strengths at 1000 h as measured by residual stress of various steels and nickel alloys (34). To convert MPa to psi, multiply...

Fig. 1. (a) Schematic diagram showing definition of case hardening and of case depth where (—) is the diameter (b) residual stress across the radius of a... 

There are many characteristics of hard cases that make their development desirable. One is wear resistance. Usually, the process is designed to develop high compressive residual stresses in the surface which counteract tensile stresses induced by the loading condition during use of the component (1) (Fig. lb). 

Figure 4 shows a typical hardness distribution (7). The case depth is considerably less than that for flame and induction hardening. The case has a high compressive residual stress, which improves the fatigue properties (8). 

The surface may gain a very high (eg, 1000 Vickers) hardness from this process. Surface deformation also produces a desired high compressive residual stress. Figure 9 illustrates the improvement in fatigue properties of a carburized surface that has been peened (18). 

Eor steel and other ferromagnetic materials, property deterrnination is more difficult. Other tests are made to measure the continuity of protective metallic coatings. Residual stresses induced in welded stmctures and in components in service owing to chemical attack may contribute to early failure. 

Both ultrasonic and radiographic techniques have shown appHcations which ate useful in determining residual stresses (27,28,33,34). Ultrasonic techniques use the acoustoelastic effect where the ultrasonic wave velocity changes with stress. The x-ray diffraction (xrd) method uses Bragg s law of diffraction of crystallographic planes to experimentally determine the strain in a material. The result is used to calculate the stress. As of this writing, whereas xrd equipment has been developed to where the technique may be conveniently appHed in the field, convenient ultrasonic stress measurement equipment has not. This latter technique has shown an abiHty to differentiate between stress reHeved and nonstress reHeved welds in laboratory experiments. 

---