# Residual stresses in an aluminum alloy

### Predition of residual stresses in an aluminum alloy due to cold expansion processes by using finite element analysis

### Chapter 1.0

### INTRODUCTION

### 1.1 Background

Pin or fastener joints are widely used in the aircraft and rotorcraft industries. These joints are also known to be susceptible to fatigue failure due to the localized stress concentrations caused by the presence of the holes. To overcome this problem, a split sleeve cold expansion process has emerged as a life enhancement method to mitigate the effect of the stress concentrations by creating a compressive circumferential residual stress ﬁeld around the hole.

### 1.2 Cold Expansion

Cold expansion system is a cost effective solution to problems associated with fatigue cracks in holes in metal structures. Cold expansion is accomplished by pulling a tapered mandrel, pre-fitted with a lubricated split sleeve, through a hole in aluminum, steel or titanium. The function of the disposable split sleeve is to reduce mandrel pull force, ensure correct radial expansion of the hole, preclude damage to the hole, and allow one-sided processing.

The process works by imparting beneficial compressive residual stress around the hole. The action of drawing the mandrel through the starting hole causes a radial plastic flow of material and results in an annular zone of residual compressive stresses that extend up to one diameter beyond the edge of the hole.

The residual stresses created by cold expansion significantly increase fatigue life by reducing the stress intensity factor and crack growth life by reducing the applied stress ratio at the hole. The magnitude of the peak residual compressive circumferential stress is about equal to the compressive yield stress for the material. The compressive stress zone spans one radius to one diameter from the edge of the hole, for diameters up to 1/2 inch for most materials. A balancing zone of tensile stresses lies beyond the circumferential compressive stress zone. The distribution of the different stresses on a hole of the typical cold working process is as shown in 1.1.

Cold Expansion is used on every commercial and military aircraft in the world because it improves the fatigue life of the structure and provides long-term operation and maintenance cost savings.

Some of the benefits include:

### * 3:1 fatigue life improvement

* Arrests small crack growth

* Cost effective alternative to redesign

* Adds no weight to structure

* Simple, one-sided operation

* Works on all common aerospace materials

* Applicable in both production and rework

* Can be automated.

Cold Expansion process uses a mandrel to pull through the sleeve and the fastener hole. Reaming of the fastener hole usually takes place after cold working, and the purpose of it is to size the hole accurately so that the intended fastener can fit in properly. The cold expansion process is as shown in 1.2.

The removal of cold worked material will reduce a segment of the residual compressive stress field and may reduce the efficiency of the CW. However such effects will depend on the amount of material removed.

In recent years, a 3D finite element analysis of cold expansion has been performed. This analysis is based on FTI's cold expansion technique and takes into account the process stages of hole expansion, hole recovery and finally finished with reaming. It was found that a 3D nature exists to the cold worked residual stress around the hole. Most importantly, it was found that the finish reaming of the material around the hole has a negligible effect on the maximum value and distribution of residual stresses. Therefore, it can be inferred from the analysis that the effect induced by reaming has been addressed through the process specifications. Therefore, the reaming performed in accordance with the technical specifications will have negligible impact on the residual stress distributions.

Reaming removes most of the initial fatigue damage and allows sizing to a specific final diameter. It is an optional although typical process.

However, there is also the possibility that the high compressive residual stresses created by cold working might be removed by the process of reaming. This might lead to a reduction in the benefits of cold working.

Although reaming of fastener holes is optional, they are usually performed. The reaming should be implemented in accordance with technical specifications.

The advantage of reaming is that it can remove the initial fatigue damage and allows sizing to a specific final diameter and hole shape. The disadvantages include the extra process step, and the risk associated with having a mechanic cut material out of a hole in an incorrect manner.

Studies have shown that the effect of reaming on the residual stress distribution of a cold worked hole is negligible when the reaming is performed in accordance with the specified process. In general, the shape of the hole may be described as hourglass, and an axial ridge will be left in the hole by the cold working process. If the joint can accommodate this condition, the hole can be left as it is. If the joint requires a more controlled hole diameter and shape, then post reaming may easily be accomplished with no perceptible effect on fatigue life.

### Chapter 2.0

### LITERATURE SURVEY

Many analytical and numerical studies were previously conducted and published regarding the prediction of the residual stresses created by cold expansion. Rich and Impellizzeri [1] and Ball [2] developed two-dimensional (2D) elastic-plastic closed form solutions for the uniform radial expansion of fastener holes assuming small displacement, plane strain, and plane stress conditions. In Refs. [4–8], 2D, 2D-axisymmetric, and 3D numerical solutions were obtained using a simpliﬁed approach, in which the hole was uniformly expanded to simulate the interference between the mandrel and the hole. The assumption of a uniform expansion inherently limits the accuracy of the predicted residual stress.

Other studies have included the mandrel insertion explicitly to model the process in a more physically realistic way. This is because the hole surface is expanded sequentially (rather than uniformly) in the actual process, starting from the mandrel entrance side toward the exit side of the hole, resulting in a variation in the residual stress magnitudes through the plate thickness.

Garcia-Grenada et al. [10] conducted a 2D-axisymmetric analysis, whereas Papinkos and Meguid [11] and Chakherlou and Vogwell [12] performed 3D simulations of cold hole expansion with the mandrel. However, none of these efforts included the sleeve in their models. In Refs. [13–15], the authors did not include the split in the sleeve, and they did not consider the friction at the interface

The frictionless contact was justiﬁed by the assumption of lubricated surfaces. However, the sleeve is only internally lubricated in the actual process. This ensures that if the hole surface is improperly cleaned after cold expansion, the installed rivets will not slide in the hole creating non desirable consequences [16].Hence, the friction at the interface between the outer surface of the sleeve and the hole is not negligible in the cold working process.

Karabin et al. [13] adopted a slightly different approach than those previously mentioned to simulate the cold expansion process and studied the inﬂuence of two different split geometries for the sleeve: conventional and overlap. They did not explicitly model the mandrel insertion and achieved the hole expansion in a circular disk by applying a uniform radial displacement on the interior surface of the split sleeve. Their study focused on the residual strains around the hole surface rather than the stress.

Wagner et al [8] described a comprehensive test programme evaluating the benefits of cold expansion for open hole specimens made of two aerospace aluminum alloys, 2024-T3 and 7075-T6. While the paper focused on the rework process for pre-cycled holes that were cold expanded on production, it also looked at the effect of cold expanding fatigue-aged plain production holes. In the case of the 2024-T3 specimens, this part of the test was conducted under constant amplitude loading at two different stress levels. At the higher stress level (193 Mpa), 30% fatigue ageing of the plain hole specimens followed by cold expansion resulted in a seven-fold improvement in fatigue life over the plain hole specimens. Furthermore, for specimens that was not cold expanded on production, cold expansion in the first 50% of the baseline life resulted in fatigue lives up to 50% greater than cold expansion at build.

Cook [9] investigated repair of cracked fastener holes by cold expansion. He looked at low-load and medium-load transfer joints in four types of aluminum under the FALSTAFF loading at two different peak stress levels. Cold expansion was applied at a range of predefined crack lengths from 0.5 to 3.0 mm. The results showed that the optimum enhancement occurred with cracks of less than about 1 mm present, but cold expansion was still effective at crack lengths up to 3.0m.

Although not directly relevant to cold expanded fastener holes in aircraft, other work on creep relaxation of residual stress has been carried out. Zhu et al. [14] studied the effect of stress relaxation during operation on fatigue crack growth in high pressure tubular reactors. The fatigue and creep fatigue crack growth in cold expanded tubes from a steam generator was reported by Ternay et al. [15] but without relating the results with the changes in residual stress. Rudin [16] studied fatigue life of aircraft engine components at high temperature but again without measuring changes in residual stress.

The current research builds upon this previous work in an effort to conduct the most sophisticated and physically realistic simulations of the cold working process. With the rapid developments in finite element methods and computer technology, numerical calculations can be carried out more efficiently and effectively for the cold expansion process. These developments will undoubtedly prove beneficial to the understanding of the process. Rigorous 3D ﬁnite element analyses (FEAs) of the cold expansion and the reaming processes are described as that which includes the friction and geometrical nonlinearities i.e. large strain. The effect of different sheet boundary conditions is discussed.

### Chapter 3.0

### INTRODUCTION TO ALLUMINIUM & ALUMINIUM ALLOYS

### 3.1 Aluminum:

Aluminum is a silverish white metal that has a strong resistance to corrosion and like gold, is rather malleable. It is a relatively light metal compared to metals such as steel, nickel, brass, and copper with a specific gravity of 2.7. Aluminum is easily machinable and can have a wide variety of surface finishes. It also has good electrical and thermal conductivities and is highly reflective to heat and light.

### 3.2 Aluminum alloys:

The mixtures of aluminum with other metals (called an alloy), often with copper, zinc, manganese, silicon, or magnesium. They are much lighter and more corrosion resistant than plain carbon steel, but not as corrosion resistant as pure aluminum. Bare aluminum alloy surfaces will keep their apparent shine in a dry environment due to the formation of a clear, protective oxide layer. Galvanic corrosion can be rapid when aluminum alloy is placed in electrical contact with stainless steel, or other metals with a more negative corrosion potential than the aluminum alloy, in a wet environment. Aluminum alloy and stainless steel parts should only be used together in water-containing systems or outdoor installations if provision is made for either electrical or electrolytic isolation between the two metals.

### 3.3 Characteristics:

At extremely high temperatures (200-250°C) aluminum alloys tend to lose some of their strength. However, at subzero temperatures, their strength increases while retaining their ductility, making aluminum an extremely useful low-temperature alloy.

Aluminum alloys have a strong resistance to corrosion which is a result of an oxide skin that forms as a result of reactions with the atmosphere. This corrosive skin protects aluminum from most chemicals, weathering conditions, and even many acids, however alkaline substances are known to penetrate the protective skin and corrode the metal.

Aluminum also has a rather high electrical conductivity, making it useful as a conductor. Copper is the more widely used conductor, having a conductivity of approximately 161% that of aluminum. Aluminum connectors have a tendency to become loosened after repeated usage leading to arcing and fire, which requires extra precaution and special design when using aluminum wiring in buildings.

Aluminum is a very versatile metal and can be cast in any form known. It can be rolled, stamped, drawn, spun, roll-formed, hammered and forged. The metal can be extruded into a variety of shapes, and can be turned, milled, and bored in the machining process. Aluminum can riveted, welded, brazed, or resin bonded. For most applications, aluminum needs no protective coating as it can be finished to look good; however it is often anodized to improve color and strength.

### 3.4 Aluminum alloy: 7075-T6

### 3.4.1 History:

Alloy 7075, a cold finished aluminum wrought product, has the highest strength of all aluminum screw machine alloys. The T6 and T651 tempers have a typical tensile strength of 83 MPa, which is higher than many mild steels. Due to its very high strength, alloy 7075 is used for highly stressed structural parts. Applications include aircraft fittings, gears and shafts, fuse parts, meter shafts and gears, missile parts, regulating valve parts, worm gears, keys, and various other commercial aircraft, aerospace and defense equipment. Rod and bar product forms can be machined on multi-spindle and CNC machining equipment.

### 3.4.2 Machining:

Alloy 7075 offers good machinability when machined using single-point or multi-spindle carbide tools on screw machines. The use of a chip breaker is recommended. The alloy is rated “B” on the Aluminum Association machinability rating system, giving curled or easily broken chips with good to excellent surface finish.

### 3.4.3 Corrosion:

Alloy 7075 has moderate corrosion resistance. The over aged T73 and T7351 tempers offer good stress-corrosion cracking resistance as compared to the T6 and T651 tempers.

### 3.4.4 Anodizing:

The anodizing response rating for 7075 alloy is good using commercially available methods. The alloy can be both hard and clear-coat anodized. The properties listed in this Alloy Data Sheet represent the best current information for this alloy. In each specific application, the user is expected to evaluate and test the alloy, temper and finishing method.

### 3.4.5 Uses:

7075 is widely used for construction of aircraft structures, such as wings and fuselages. Its strength and light weight are also desirable in other fields. Rock climbing equipment, bicycle components, and hang gliders are commonly made from 7075 aluminum alloy. The bicycle industry is also using 7005 and 6061 aluminum alloys. Hobby grade R/C's commonly use 7075-T6 and 6061 for chassis plates. One interesting use for 7075 is in the manufacture of M16 rifles for the American military. It is also commonly used in shafts for lacrosse sticks.

Due to its strength, low density, thermal properties and its polishability 7075 is widely used in mould tool manufacture. This alloy has been further refined into other 7000 series alloys for this application namely 7050 and 7020.

### 3.4.6 Typical Physical/Mechanical Properties:

Density : 2600-2800 kg/m3

Melting Point : 660 °C

Elastic Modulus : 70-79 GPa

Poisson's Ratio : 0.33

Tensile Strength : 570 MPa

Yield Strength : 505 MPa

Percent Elongation : 10-25%

Thermal Expansion Coefficient : 20.4-25.0 × 10-6 /°C

### Chapter 4.0

### NON LINEAR MATERIAL PROPERTIES

### 4.1 Introduction

Non linear material properties are usually tabular data, such as plasticity data (stress-strain curves for different hardening laws), magnetic field data (B-H curves), creep data, swelling data, hyper elastic material data, etc.

The automatic time stepping feature [AUTOTS] will respond to plasticity after the fact, by reducing the load step size after a load step in which a large number of equilibrium iterations was performed or in which a plastic strain increment greater than 15% was encountered. If too large a step was taken, the program will bisect and resolve using a smaller step size.

Other kinds of nonlinear behavior might also occur along with plasticity. In particular, large deflection and large strain geometric nonlinearities will often be associated with plastic material response. If you expect large deformations in your structure, you must activate these effects in your analysis with the NLGEOM command.

### 4.2 Plastic Material Options:

### 4.2.1 Bilinear Kinematic Hardening

The Bilinear Kinematic Hardening option assumes the total stress range is equal to twice the yield stress, so that the Bauschinger effect is included. This option is recommended for general small-strain use for materials that obey von Mises yield criteria (which includes most metals). It is not recommended for large-strain applications.

### 4.2.2 Multi linear Kinematic Hardening

The Multi linear Kinematic Hardening options use the Besseling model, also called the sub layer or overlay model, so that the Bauschinger effect is included. Kinematic Hardening is preferred for use over Multi Linear hardening because it uses Rice's model where the total plastic strains remain constant by scaling the sub layers.

### Chapter 5.0

### FINITE ELEMENT METHOD

### 5.1 Introduction

The Basic concept in FEA is that the body or structure may be divided into smaller elements of finite dimensions called “Finite Elements”. The original body or structure is then considered as an assemblage of these elements connected at a finite number of joints called “Nodes” or “Nodal points”. Simple functions are chosen to approximate the displacements over each finite element. Such assumed functions are called “shape functions”. This will represent the displacement within the element in terms of the displacement at the nodes of the element.

The Finite Element Method is a mathematical tool for solving ordinary and partial differential equations. Because it is a numerical tool, it has the ability to solve the complex problems that can be represented in differential equations form. The applications of FEM are limitless as regards the solution of practical design problems.

In the recent years, FEA has been universally used to solve structural engineering problems .The departments, which are heavily relied on this technology, are the automotive and aerospace industry. Due to the need to meet the extreme demands for faster, stronger, efficient and lightweight automobiles and aircraft, manufacturers have to rely on this technique to stay competitive.

### 5.2 Basic steps involved in FEA

Mathematically, the structure to be analyzed is subdivided into a mesh of finite sized elements of simple shape .within each element, the variation of displacement is assumed to be determined by simple polynomial shape functions and nodal displacements. Equations for the strains and stresses are developed in terms of the unknown nodal displacements. From this, the equations of equilibrium are assembled in a matrix stiffness equation. Once the nodal displacements are known, element stresses and strains can be calculated. This is a numerical solution for obtaining solution to many of the problems encountered in engineering analysis.

* Discretisation of the domain

* Application of Boundary conditions

* Assembling the system equations

* Solution for system equations

* Post processing the results.

The Finite Element Method is a very important tool for those involved in engineering design, it is now used routinely to solve problem in the following areas.

* Structural analysis

* Thermal analysis

* Vibration and Dynamics

* Buckling analysis

* Acoustics

* Fluid flow simulation

* Crash simulation

* Mould flow simulation

### 5.2.1 Descritization of the domain:

The task is to divide the continuum under study into a number of subdivisions called elements. Based on the continuum it can be divided into line or area or volume elements.

### 5.2.2 Application of boundary conditions:

From the physics of the problem we have to apply the field conditions i.e. loads and constraints, which will help us in solving for the unknowns.

### 5.2.3 Assembling the system equation:

This involves the formulation of respective characteristic (Stiffness in case of structural equation of matrices and assembly.

### 5.2.4 Solution for system equations:

Solving for the equations to know the unknowns. This is basically the system of matrices which are nothing but a set of simultaneous equations that are solved.

### 5.2.5 Viewing the results:

After the completion of the solution we have to review the required results.

### 5.3 How FEA can be used

### 5.3.1 Design Validation:

FEA was being used in initial days, to evaluate the design against the intended purpose. In this method attempts were made to simulate a test condition and then study the results of FEA to assess whether the design meets the requirements or not. If the simulations revel that the design might fail, then the engineer would modify the design to avoid failure. This method was helping to avoid the design validation through testing of prototypes. This approach was used by experienced engineers, who were used to design the equipment by conventional approaches, but want to avoid testing.

### 5.3.2 Design guidance:

As the technique is gradually evolved, the engineering community has slowly started believing in FEA and the tremendous advantages it offers. Increasingly the engineering community started this tool to study the characteristics of a design than to just simulate the test conditions. By this approach, the conceptual designer can start with a basic shape, evaluate the design, find out the weak zones and comes out with the design improvements. By this way FEA guides the design engineer that, where he can remove the material and where he need to add strength.

### 5.3.3 Design optimization:

At later stage, when the FEA tools become more powerful, optimization algorithms have been embedded into the FEA tools thus improving the power of FEA, An FEA software integral with optimization tools can be used in design optimization.

### 5.4 Introduction to ANSYS

ANSYS finite element analysis software enables engineers to perform the following tasks:

* Build computer models or transfer CAD models of structures, products, components, or systems.

* Apply operating loads or other design performance conditions.

* Study physical responses, such as stress levels, temperature distribution, or electromagnetic fields.

* Optimize a design early in the development process to reduce production costs.

* Do prototype testing in environments where it otherwise would be undesirable or impossible

The ANSYS program has a compressive graphical user interface (GUI) that gives users easy, interactive access to program functions, commands, documentation, and reference material. A graphical user interface is available throughout the program, to guide new users through the learning process and provide more experienced users with multiple windows, pull-down menus, dialog boxes, tool bar and online documentation.

### 5.4.1 Organization of the ANSYS program:

The ANSYS program is organized into two basic levels:

* Begin level

* Processor (or Routine) level

The beginning level acts as a gateway in to and out of the ANSYS program. It is also used for certain global program controls such as changing the job name, clearing (zeroing out) the database, and copying binary files. At the processor level several processors are available; each processor is a set of functions that perform a specific analysis task. For example, the general preprocessor (PREP7) is where we build the model, the solution processor (SOLUTION) is where we apply loads and obtain the solution, and the general postprocessor (POSTI) is where we evaluate the results and obtain the solution.

### 5.4.2 Performing typical analysis:

The ANSYS program has many finite element analysis capabilities, ranging from a simple, linear, static analysis to a complex, nonlinear, transient dynamic analysis.

### 5.4.2.1 Steps Involved in FE Analysis

* Build the model

* Apply loads and obtain the solution

* Review the results

### Table 5.1 Description of steps followed in each phase.

Pre-Processor

Solution Processor

Post-Processor

Assigning element type

Analysis definition

Read results

Geometry definition

Constant definition

Plot results on graphs

Assigning real constants

Load definition

View animated results

Material definition

Solve

Mesh generation

Model display

### 5.5 Pre-processor:

The input data for an ANSYS analysis are prepared using a prepared using a preprocessor. The general preprocessor (PREP 7) contains powerful solid modeling and mesh generation capabilities, and is also used to define all other analysis data with the benefit of date base definition and manipulation of analysis data. Extensive graphics capability is available throughout the ANSYS program, including, including isometric, perceptive, section edge and hidden-line displays of three dimensional structures, results, and contour displays of solution results.

The pre-processor stage involves the following:

* Specification of the title.

* Setting the type of analysis to be used, e.g., Structural, Thermal, Fluid, or electromagnetic, etc.

* Creating the model, the model may be created in pre-processor, or it can be imported from another CAD drafting package via a neutral file format.

* Defining element type, these chosen from element library.

* Assigning real constants and material properties like young's modules, Poisson's ratio, density, thermal conductivity, damping effect, specific heat, etc.

* Apply mesh; Mesh generation is the process of dividing the analysis continuum into number of discrete parts of finite elements.

### 5.6 Solution processor:

Here we create the environment to the model, i.e., applying constrains & loads. This is the main phase of the analysis, where the problem can be solved by using different solution techniques. Her three major steps involved.

* Solution type required, i.e., static, modal, or transient etc., is selected.

* Defining loads. The loads may be point loads, surface loads; thermal loads like temperature, or fluid pressure, velocity are applied.

* Solve FE solver can be logically divided in o three main steps, the pre-solver, the mathematical- engine and post-solver. The pre-solver reads the model created by pre-processor and formulates the mathematical representation of the model and calls the mathematical engine, which calculates the result.

### 5.7 Post – processor:

It is probably the most important step in the analysis, because we are trying to understand how the applied loads affects the design, how food your finite elements mesh is, and so on. The analysis results are reviewed using postprocessor, which have the ability to display distorted geometries, stress and strain contours, vector field displays, mode shapes and time history graphs. The results of the solution are

1. Nodal degree of freedom values, which form the primary solution.

2. Derived values which form the element solution.

### 5.8 Advantages:

* Avoid the creation of expensive prototype modeling

* Economy in terms of time and money

* Very complex model can be solved with greatest ease

* Any change in the model can be easily incorporated

* Helps in optimization of the product

* Any type of optimization can be performed

* Extension graphic capabilities

### 5.9 Limitations:

* This method is an approximate one and doesn't give exact solution.

* Storing of large data.

* User judgment is very essential.

* Aspect ratio should be carefully maintained to give higher accuracy.

* The user should have good interpreting capabilities.

### Chapter 6.0

### FE SIMULATION OF COLD EXPANSION PROCESS

### 6.1 Modeling

The geometric modeling of the cold expansion work piece is performed in ANSYS 11.0. The geometric details of the work piece considered for the analysis is given below:

Length of the work piece, L = 25.4 mm

Width of the work piece, w = 25.4 mm

Thickness of the work piece, t = 2.04 mm

Initial Diameter of the hole, di = 6.15 mm

Final Diameter of the hole, do = 7.26 mm

The Geometric model of the cold expansion work piece is as shown in 6.1.

### 6.2 FE Modeling

ANSYS 11.0 is used to carry out the numerical simulations. The following section explains the different steps involved in the FE Modeling of the work piece for the cold expansion process.

### 6.2.1 FE Descritisation / Meshing

FE descristisation is performed in ANSYS 11.0 using 8 node SOLID 185 brick element. The FE Model details of the cold expansion of work piece are as follows:

Number of nodes: 16346

Number of elements: 13970

The model considered for the analysis is only a half model as it is symmetric as shown in 6.2. Fine mesh is used near the hole to capture the results. FE Model is as shown in 6.3.

### 6.2.2 Material Properties:

The sheet material considered for the analysis is 7075T6 Aluminum alloy with the properties as given below:

Young's Modulus : 72500 MPa

Poisson's Ratio : 0.3

Density : 2.79*10-6 Kg/mm3

Using these data, Multi linear Kinematic Hardening material modeling is considered for the analysis. 6.4 shows the stress strain diagram for the Multi linear Kinematic Hardening Model utilized for the analysis.

A detail of the Multi linear Kinematic Hardening is discussed in Section 4.2.2 of the same report.

### 6.2.3 Boundary Conditions

Following are the boundary conditions used in the FE Model:

a. Symmetric Boundary Conditions

b. Rigid Body Boundary Conditions

Symmetric Boundary Conditions:

The FE Model considered is a symmetric model hence nodes in the plane normal to the symmetric plane is restricted for the symmetric plane. The symmetric boundary conditions are as shown in 6.5.

### Rigid Body Constraints:

coldexp1025The edges of the FE Model are constrained in the Z direction. In order to avoid the rigid body movement of the model the rigid body constraints of X direction on all the 8 corners are used. The rigid body constraints are as shown in 6.5.

### 6.2.4 Loads

Cold Expansion process can be broadly divided into three steps:

1. Hole Expansion

2. Hole Recovery

3. Finish Reaming

In the first step the higher diameter axial movement of the mandrel applies a uniform radial pressure on the face of the hole. The expectation of the force or pressure due to this process is a tedious task. As per the FTI specification in this step the hole expands by 4%. As per the specifications of the work piece the following calculation is performed to find the diameter of the hole after the first step.

Initial Diameter of the hole, di = 6.15 mm

% Expansion on the hole, = 4 %

Let,

Intermediate Diameter of the hole, dim = x mm

Therefore,

x-6.15=.04x

0.96x=6.15

Hence, x= 6.40625 mm

The displacement to be applied on the face will be,

D =dim-di

= 6.40625 – 6.15

= 0.25625 mm

Therefore a radial displacement of 0.25625mm is applied on the face of the work piece. A cylindrical coordinate system (CSYS,12) is created with radial direction as X, longitudinal direction as Z and tangential direction as Y. The face nodes are rotated into the CSYS 12. The radial displacements are as shown in 6.6.

To simulate the second step i.e. release of the hole, the displacements are removed to simulate the release of the loading on the face.

To simulate the third step i.e. the reaming the elements in the range of the final diameter are killed using the EKILL option in ANSYS 11.0 which makes these elements inactive during the process.

### 6.2.5 Solution options:

Following are the solution options considered for the analysis:

Maximum number of sub steps : 50

AUTO Time Step : On

Time at end of step 1 : 1

Time at end of step 2 : 2

Time at end of step 3 : 3

NLGEOM : On

(This command controls the load direction before and after the deflection)

The three steps are solved for the three steps and the results are presented in 7.0 section of this report.

### Chapter7.0

### RESULTS & DISCUSSIONS

In this chapter presentation of the results for the following load steps are presented. The directional results for the following load steps are presented in the local cylindrical coordinate system (CSYS=12)

1. Hole Expansion

2. Hole Release

3. Reaming

The 4% hole expansion process is simulated by applying a radial displacement on the hole surface which is due to the axial movement of the mandrel. In this chapter the deformation and stress contours in the local coordinate system (CSYS12) is provided.

### 7.1 Hole Expansion Process

### 7.1.1 Displacement Plots

### 7.2 Hole Release

The second step in the cold expansion is the release of hole which is 4% hole expanded. Hence the applied radial displacement is made zero to the effect of hole expansion. In this section 7.2, the deformation and stresses plots in the cylindrical coordinate system (CSYS 12).

### REFERENCES

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19. FTI Process Specification 8101C – Cold expansion of holes using standard split sleeve system and countersink cold expansion, Fatigue Technology Incorporated (FTI) of Seattle USA.