Seikh to the Indian Institute of Technology Guwahati for the award of the degree of Doctor of Philosophy has been done under my supervision in Technology Guwahati. In this thesis, a theoretical and experimental study of the thermal autofrettage process is carried out.
The Autofrettage process
The hydraulic autofrettage uses ultra-high hydraulic pressure on the inner wall of the cylinder to achieve the desired degree of plastic deformation. The thermal autofrettage process is introduced in Section 1.6, along with the scope and objective of this thesis.
Hydraulic Autofrettage
This results in residual compressive stresses on and around the inner wall of the cylinder. In addition, any leakage of hydraulic oil during the self-fretting process is harmful to the environment.
Swage Autofrettage
Therefore, the contact between the mandrel and cylinder must be lubricated to reduce sliding friction (O'Hara, 1992). However, the pressure required to drive the piston increases with the increase in the size of the mandrel (Iremonger and Kalsi, 2003).
Explosive Autofrettage
This greatly increases the pressure of the energy transfer medium, which is confined between the radial piston and the inner wall of the cylinder. After the explosively created pressure has dissipated, significant residual pressure ring stresses are created on and around the inner wall of the cylinder.
Key Issues in Autofrettage Processes
The level of overstress in an autolocked cylinder is another important influencing factor affecting residual stresses. The level of overstress is a function of the radial position up to which plastic deformation is reached by the autofrettage load in the interior of the cylinder, referred to as the radius of the elastic-plastic interface.
Scope and Objective of the Present Work: Thermal Autofrettage …. 8
The primary goal of the thesis is to theoretically and experimentally study thermal self-fretting. The importance of the works presented in this thesis lies in the simplicity of the proposed process of thermal self-fretting.
Modelling of Hydraulic Autofrettage Process
- Analytical Models Assuming Elastic-perfectly Plastic
- Large Strain Solutions
- Autofrettage Level after Machining
- Modelling considering Strain Hardening and Bauschinger
- Modelling Based on Strain Gradient Plasticity Theory
- Finite Element Method and Finite Difference Method Based
- Optimization of Autofrettage Pressure
He studied the influence of the Bauschinger effect and hardening on the residual stress distribution. The author observed that both the stiffening effect and the Bauschinger effect influence the residual stress distribution of the surround in the cylinder bore.
Modelling of Swage Autofrettage Process
Stacey and Webster (1988) performed the experimental determination of residual stresses in hydraulically sealed AISI 4333M4 steel cylinder by the boring Sachs method and neutron diffraction. The determination of residual stresses in hydraulic autofretting steel cylinders using the Sachs boring method was carried out by Venter et al.
Fatigue Life Analysis of Autofrettaged Cylinders
The stress intensity factor was then used in Paris law to estimate the fatigue life. Authors observed that the fatigue life of the autofrettage cylinder is more than the non-autofrettage cylinder for a range of working pressures.
Study of the Autofrettage Process Combined with Shrink-fit
They investigated the effect of crimp fit tolerance for different overstrain percentages of the autosuspension on the residual hoop distortion. They concluded that the increase in crimp fit tolerance is detrimental to the combined process.
Elasto-plastic Thermal Stress Analysis
The temperature was assumed constant in the core of the cylinder and in its outer part, decreasing to the reference temperature at the surface. Further yielding of the cylinder wall with increased thermal loading was considered to analyze the fully plastic condition.
Study of Thermal Autofrettage
Research Gap and Detailed Objectives of the Present Thesis
In this paper, a method of achieving thermal autofrettage in thick-walled cylinders by creating radial thermal gradients in the cylinder wall thickness is proposed. Experimental study of the thermal autofretting process: A detailed experimental study of the thermal autofretting process for thick-walled cylinders will be carried out in this thesis.
Introduction
None of the existing literature studies the thermal autofrets of thick-walled cylinders or discs theoretically or experimentally. Sufficiently high thermal stress can cause plastic deformation in a portion of the wall of the cylinder or disc.
Thermal Stress Analysis in the Disk
Solution for Thermo-elastic Stresses
Taking zero temperature as reference and using generalized Hook's law, the radial and hoop stresses under plane stress conditions for a purely elastic body at temperature T are given as (Noda et al., 2003). For radial displacement u as a function of r, the radial and hoop stresses are given by (Chakrabarty, 2006).
The Thermo-elasto-plastic Behaviour of the Hollow Disk.… 56
- Plastic zone: a≤r≤c
During the first phase of elasto-plastic deformation, a portion of the inner wall of the disk becomes plastic up to a radius c and beyond c the outer wall remains in the elastic state. The second phase of elasto-plastic deformation remains in the wall of the disk as long as the temperature difference is not large enough to cause the plastic deformation of the entire wall.
Analysis of the Second Stage of Elasto-plastic Deformation
- Intermediate elastic zone: c≤r≤d
- Inner plastic zone: a≤r≤c
- Outer plastic zone: d≤r≤b
To find the solution for the radial thermal stress in the inner plastic zone (a≤r≤c), the differential equation Eq. 3.21) and using the boundary condition, σr at r=c from the elastic zone c≤r≤d (Eq. 3.38), we obtain an expression for the radial thermal stress as Substituting the value of D from Eq. 3.51), the total component of the deformation of the ring in the plastic zone d≤r≤b is obtained as
Residual Thermal Stresses
Residual Stresses During the First Stage of Elasto-plastic
Residual Stresses During the Second Stage of Elasto-plastic
The residual radial thermal stress in the inner plastic zone (a≤r≤c), is obtained by Eq.
Solution Methodology
In the outer plastic zone (d≤r≤b), the residual thermal stresses are obtained by subtracting Eqs. the radial stress in the inner radius during the first stage of elasto-plastic deformation provides. 3.64) will give the value of the unknown radius c. The halving method for solving the nonlinear equation is described in Appendix A. However, during the second phase of elasto-plastic deformation, initial estimates for c & d, obtained by making K=0 in Eqs. 3.65) and (3.66) and their solution for c & d using the FSOLVE (least square method for solving simultaneous nonlinear equations) function in MATLAB.
Conceptual Design of a System for Creation of Thermal Gradient in
The average temperature can be taken as the mean value of the fluid's inlet temperature Ti and outlet temperature To. The value of h can be calculated using Eqs and the temperature of the inner surface Ta can be estimated from Eq.
Numerical Simulations
Case of Aluminum Disk
- Elasto-plastic thermal stress pattern
- Residual stress pattern
- Overall stresses with and without autofrettage
For the temperature difference of 80 °C, the maximum tensile residual stress is generated at the interface between elastic and plastic (at r=c). For the temperature difference of 100 °C, the maximum residual stress occurs at the outer radius.
Case of Mild Steel Disk
- Elastic-plastic thermal stress pattern
- Residual stress pattern
- Overall stresses with and without autofrettage
The magnitudes of residual tensile stresses generated at the outer region of the disc are very small. Therefore, surge of the disk during compression will first occur at the elastic-plastic interface.
Summary
In the case of the autofrettage disc, the magnitude of the maximum equivalent Tresca stress is found to be 18.82% less than that in the case of the disc without autofrettage during pressurization. Compared to hydraulic and swage autofrettage, the achievable level of autofrettage is limited by the maximum allowable temperature at the outer wall of the disc.
Introduction
This motivates the modeling of thermal autofrettage for thick-walled cylinders taking into account the general plane deformation state. In this chapter, the thermal autofrettage process is analyzed theoretically for thick-walled cylinders, taking into account the general plane strain condition.
Thermal stress analysis
Solution for thermo-elastic stresses
Using generalized plane stretching conditions (εz=constant=ε0), Eq. 3.4) and the use of strain compatibility Eq. 3.6), the solution for radial stresses and hoop stresses is given by. The constant axial strain ε0 can be determined from the condition of the free end (zero total axial force), given by. 4.14), the constant axial strain is obtained as.
Initiation of Yielding
4.18) at r=a, the temperature difference required for the onset of yielding in the inner radius is obtained as.
Analysis of the First Stage of Elasto-plastic Deformation…
- Plastic zone I: a≤r≤c
- Plastic zone II: c≤r≤d
- Elastic zone: d≤r≤b
Thus, Tresca provides the yield criterion for a non-hardening cylinder. 4.20) in equilibrium equation (Eq. 3.6) the radial thermal stress in the plastic zone I is obtained as. where C3 is a constant of integration. 4.20), the thermal hoop and axial stresses are obtained as. Substituting the values of C1 and C2 into Eq. 4.7) and (4.8), the resulting elastic radial and hoop stress distributions in the elastic zone are obtained as. 4.4), the axial stress distribution is obtained as
Residual Stress Distribution in the First Stage of Elasto-
Constant axial strain ε0 for the generalized plane strain included in the various stress–strain equations during the first stage of elastoplasticity.
Evaluation of Constants and Solution Methodology
The constant axial stress ε0 is obtained using the free end condition (zero total axial force) given by. plastic zone I) (plastic zone II) (elastic zone). To find the values of the limit radii, c and d, the radial vanishing strain boundary conditions in the inner radius and (plastic zone II) (plastic zone II). 4.75) and (4.76) are solved simultaneously using the FSOLVE function in MATLAB to obtain the values of c and d.
Analysis of the Second Stage of Elasto-plastic Deformation
- Elastic zone: d≤r≤e
- Plastic zone III: f≤r≤b
- Plastic zone IV: e≤r≤f
Substitution of the expressions for C1 and C2 in Eq. 4.7) and (4.8), the resulting elastic radial and hoop stresses are obtained as. 4.4), the axial stress distribution is given by By using the strain-displacement relation (Equation 3.4) and generalized Hook's law (Equations 4.1 and 4.2) the following differential equation is obtained: 4.99), the radial displacement u is obtained as.
Residual Stress Distribution in the Second Stage of Elasto-
The plastic part of the hoop stress component is obtained by subtracting the elastic part from the total hoop stress component and is given by.
Evaluation of Constants and Solution Methodology for the
To find the constant C7, the boundary condition, at r=f, (plastic zone III) (plastic zone IV). Using vanishing radial stress boundary conditions on the outer beam and (plastic zone IV) (plastic zone IV).
Conceptual Design of a System for Creation of Thermal Gradient in
Since the difference in temperature between the inner and outer surface of the cylinder is 120 ºC, the value of outer surface temperature Tb is 157.91 ºC.
Numerical Simulations
Case of aluminum cylinder
- Elastic-plastic thermal stress distribution
- Residual thermal stress distribution
It can be seen that the magnitude of the radial stresses is quite small compared to the magnitude of the annular and axial stresses in the cylinder. It is observed that the maximum Tresca equivalent stress (|σθ−σr|/2, in this case) occurs at the radius of the plastic-plastic interface (r=c) in the self-fretted cylinder.
Case of SS304 cylinder
- Elastic-plastic thermal stress distribution
- Residual thermal stress distribution
- Overall stress distribution with and without
Upon cooling to room temperature, a significant amount of compressive residual thermal rings and axial stresses are generated on and around the inner radius of the SS304 cylinder. The cylinders are not subjected to the second stage of elastoplastic deformation due to the restriction to (Tb−Ta), i.e. the maximum temperature Tb does not exceed the recrystallization temperature of the material.
Influence of Strain Hardening
Strain Hardening in First stage of Elasto-plastic
Using first condition of Eq. 4.124) into equilibrium equation (Eq. 3.6), integration of the resulting equation provides the radial stress axis. where εeqp is a function of radius and r1 is a dummy variable. The procedure involves an iterative approach to estimate the values of c and d. The numerical solution procedure is described as follows:
Strain Hardening in Second stage of Elasto-plastic
4.130) provides the updated values of εeqp at each radial position in the plastic zone I. 4.133), the values of εrpat at different radial positions in the plastic zone II are updated. The updated values of εeqp at different radial positions in plastic zone II are obtained from Eq.
Numerical Comparison of Stresses with and without Strain
The elastoplastic strains generated in the cylinders are numerically simulated for both non-hardening and strain-hardening cases. Due to strain hardening, the stresses in the plastic zones are slightly higher than the stresses without strain hardening.
Summary
The simulation results reveal encouraging trends of residual stresses in the cylinders, which is similar to the case of hydraulic autofrettage. The effect of strain hardening is also included in the solutions using Ludwik's hardening law.
Introduction
Therefore, this work attempts to develop a criterion based on the ratio of cylinder wall length to wall thickness for the applicability of analytical models. The results of the FEM analysis are compared with analytical plane stress and generalized plane strain models.
Problem definition
However, there is no quantification of the cylinder length up to which these analyzes are applicable. The main objective of FEM analysis is to develop a dividing line between analytical models based on the length to wall thickness ratio, L/(b−a) of the cylinder.
Three-Dimensional Finite Element Modelling
- Material Properties
- Boundary Conditions and Mesh Generation
- Mesh Sensitivity Analysis
- Comparison of 3-D Finite Element Elasto-plastic Thermal
The thermo-elasto-plastic stresses generated in the cylinder are analyzed by varying the length of the cylinder. A comparative study with the models for plane stress and generalized smooth deformations is presented for different length and wall thickness ratios for the cylinder in section 5.3.4.
Finite Element Residual Thermal Stress solutions
The results are shown in Figure 5.4 together with the predictions of generalized plane strain model for L/(b−a)=10 and plane stress model for L/(b−a)=0. The analytical predictions of the residual stress are obtained assuming that the unloading process is completely elastic as presented in Chapters 3 and 4.
Effect of Strain Hardening
It is noted that the finite element predictions of the residual stresses closely match the analytical models for the respective L/(b−a) ratio of the cylinders. The stresses in the stress-hardened cylinders deviate by less than 5% compared to the stresses in the cylinders without stress-hardening.
Summary
A typical comparison of the FEM elastoplastic strains in the aluminum cylinder with the generalized plane strain and plane stress models is shown for L/(b−a) = 10 and 0.5, respectively. Finite element simulations are also performed for aluminum and SS304 cylinders with and without strain hardening by obtaining appropriate lengths corresponding to the generalized plane strain and plane stress state.
Introduction
In section 6.5, the residual stresses in the cylinder are derived on the basis of the Vickers microhardness test. In Section 6.6, the opening angle measurement method is presented to verify the presence of residual stresses in the cylinder.
The Experimental Setup for Achieving Thermal Autofrettage
This provides an additional safety advantage compared to the hydraulic self-fretting process. The process involves the flow of cold water, the leakage of which is not harmful to the environment.
A Brief Description of the Sachs Boring Method
The desired temperature difference across the cylinder wall thickness can easily be created in the developed setup. Fb, Fr are the cross-sections of the original cylinder and the bored-out cylinder, respectively, given by
Results of Sachs Boring Method Along With Comparison with the
Materials
The materials of the cylinders subjected to thermal self-fretting were stainless steel SS202, SS304 and mild steel.
Measurement of Sachs Boring
During processing, the guide wires from the strain gauges were wound around the circumference of the chuck of the lathe and fixed on the circumference with the help of adhesive tape. After recording the voltage data, the guide wires were disconnected and reattached at the circumference of the chuck.
Evaluation of Residual Stresses Using Sachs Boring Data
Residual stresses are also evaluated using an analytical generalized plane strain model and compared with experimental results. Figures and 6.7 show that the experimental residual stresses of the Sachs well are in good agreement with the residual stresses predicted by the general plane strain model.
Inference of Residual Stresses from Microhardness Test
The average microhardness of the non-auto-etched cylinder on the outer surface is 170.64 HV with a standard deviation of 5.25. On the inner surface of the non-auto-etched cylinder, the average microhardness is 174.69 HV with a standard deviation of 4.13.
Demonstration of Residual Stresses by the Measurement of Opening
Summary
Introduction
Comparison of the Maximum Pressure Carrying Capacity of
Parametric Study of Thermal and Hydraulic Autofrettage
Effect of Eα and σ Y
- Autofrettage of cylinders for low σ Y /(Eα) materials
- Autofrettage of cylinders for high σY/(Eα) materials 189
Case 1: Cylinders Subjected to Thermal Gradient in which the
Hydraulic Autofrettage of Cylinders Subjected to Thermal
Thermal Autofrettage of Cylinders Subjected to Thermal Gradient
Summary
Introduction
Shrink fitting of an outer cylindrical layer to the thermally
Numerical Results and Discussion
A Comparison of the Effect of Shrink-fit on Hydraulic and Thermal
Fatigue Life Analysis
Calculation of Stress Intensity Factor
- Thermally autofrettaged cylinder with shrink-fit
- Thermally autofrettaged monobloc cylinder
- Non-autofrettaged monobloc cylinder
Calculation of Fatigue Life
Summary
Conclusions
Scope for Future Work
