Fundamentals of Vibratory Stress Relief

INTRODUCTION

Manufacturing processes such as casting and welding leave residual stresses within a part which are capable of causing dimensional changes (Qinghua et al., 2008). These residual stresses can accelerate corrosion and crackingand reduce strength and fatigue life of the part when combined with service loads (Bonal Technologies Inc., 1992) (Lulgjuraj, 1996; Welding Consultants Inc., 1990). Using Vibratory Stress Relief (VSR) to reduce these residual stresses has many advantages over the heat treatment methods (Landgraf et al., 1967; Krempl, 1967; Sandor, 1972). Some of the advantages include: the equipment required for running the process is inexpensive and easy to use, potential saving in cost is associated with the process over heat treatment annealing due to decreased process time and energy consumption, no scaling results from the treatment, any size of part can be relieved using this technology provided that it is isolated, bringing the process to the workpiece minimizes handling costs, the process is cleanand no ventilating or air-scrubber equipment is needed since VSR generates no smoke, fumes, or gases.

VSR studies were done on heavy fabrication (Ohol et al., 1988), welded parts (Bouhelier et al., 1988), titanium blocks (Volkov and Orzhekauskas, 1988), Vibratory Weld Conditioning (VWC) on welded body valves (Xu et al., 2007; Qinghua et al., 2008), cyclic loading on stainless steel welded parts proved effectiveness (Rao et al., 2007), computer simulation for vibrator stress relief by mean of cyclic loading proved that time has no effect on residual stress relief (Zhao et al., 2008)and cyclic loading extended the life of fatigue tests (Tuegel and Brooks, 1997). The most interesting study as far as results and data documentation was done by Wozney and Crawmer (1968). Although, Wozney and Crawmer results were important, there is much more work that can be done in this area to better understand the process. A mathematical model can be developed to help predict the residual stress relief. Commercial VSR equipment can be used instead of a fatigue test machine and fatigue limit of the specimen should be considered as an important factor of VSR.

To help understand the VSR process, fundamentals of cyclic loading such as stress controlled and strain controlled functions, cycle dependent hardening of the materialand the Bauschinger effect were studied in detail (Lubhan and Felgar, 1961; Sachs et al., 1948; Ludwik and Scheu, 1923; Beer and Johnston, 1981; Hebel Jr., 1985; Dieter, 1986; Measurements Group, 1993). The original residual stress distribution in a rectangular bar is known. The distribution of residual stress after bending is analyzed based on superimposing an applied load and its inverse (Sandor, 1972).

Tensile tests were performed to experimentally determine the material properties of the specimens used in the experiments. Using the hole drilling technique, the distribution of the initial residual stress in the specimens was measured before the vibration test. These distributions were identical in form with a small difference in magnitude. Several specimens were vibrated according to different parameters. The final residual stress distributions in these specimens were measured after vibration using the hole drilling technique.

Experimental procedure and equipment
Tensile test: Four specimens of the ASTM A36 hot rolled steel 457.2x25.4x9.52 mm material used in the vibratory stress relief experiments were tensile tested. The yield point and modulus of elasticity were found experimentally using an Instron tensile testing machine and compared to handbook values Table 1.

VSR equipment: VSR equipment as shown in Fig. 1

Table 1:	Handbook and experimental values of ASTM-A36

Fig. 1:	VSR equipment

VSR tests: A resistance strain gage was installed on the top surface of each bar, 127 mm from the end as shown on ure 2. This strain gage was used to monitor the cyclic strain amplitude during vibration. A SOMAT field computer system was used to display and record the strain data for each sample in real time. A length of 76.2 mm of the specimens is clamped to the vibrating bedand the remainder of the specimen was cantilevered. A manual regulator was used to control the speed of the motor. A strobe light was used to record the vibrating frequency of the bar at the desired surface strain amplitude.

Tests to determine influence of No. of cycles: In these tests the specimens were vibrated with the following parameters as the surface strain amplitude is fixed at±1050 με for 20,000 and 100,000 cycles Table 4 .

Tests to determine influence of cyclic strain amplitude: In these tests the specimens were vibrated with the following parameters as the number of cycles is fixed based on the results of the previous test and the surface strain amplitude used, were 550, 1050 and 1550 με Table 5.

Table 2:	Reduction in residual stress in the X and Y directions after VSR

Table 3:	Percentage stress reduction.

Table 4:	Test to determine influence of No. of cycles

Table 5:	Tests to determine influence of cyclic strain amplitude

Tests to determine the influence of VSR on residual stress reduction: A total of fourteen specimens were used to determine the influence of VSR on residual stress reduction Table 6.

Theory and analysis: Prediction of remaining residual stress after one half strain cycle:

Loading and unloading between the two strain ranges ±1550με and ±1350με is shown in Fig. 2.

The compressive stress (Sandor, 1972) increases from its initial value σ_initial to the yield strength. Since the fixed strain is higher than the elastic strain, plastic flow occurs. On unloading from the compression half of the cycle, the behavior will be elastic and σ_final is reached.

Using a straight line equation with the slope equals to Eq. 1

(1)

And by simple calculation from the geometry of Fig. 3 we can obtain the following equations:

(2)

(3)

(4)

Fig. 2:	Strain gages locations

Fig. 3:	Bending the bar in the first half cycle

where σ_flow= σ_y for perfectly plastic materials and σ_flow= kεⁿ for strain hardening materials.

Calculation of residual stress reduction in the X and Y directions, along the length 457.2 mm and the width 25.4 mm of the bar are the three strains ε₁, ε₂and ε₃ at 0, 60 and 90° angles, respectively, were read directly from the strain gage indicators for every increment of the hole drilling. Data reduction sheets were used to calculate the maximum stresses σ_max and σ_min and their directions (Measurements Group, 1993). From these maximum stresses the principle stresses σ₁ and σ₂ were calculated along with their directions. Finally σ_x and σ_y were calculated from σ₁ and σ₂.