2006 int ansys conf 43

7/29/2019 2006 Int Ansys Conf 43

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Analysis of 3D Cracks in an Arbitrary Geometry withWeld Residual Stress

Greg Thorwald, Ph.D.

Ted L. Anderson, Ph.D.Structural Reliability Technology, Boulder, CO

Abstract

Materials containing flaws like inclusions and lack of weld fusion can cause cracks to form and grow; acritical size crack can cause a catastrophic fracture failure, even at low stress. Fracture mechanics allows

cracks to be evaluated as benign or requiring repair. Modeling the actual crack location in a complicated

geometry is necessary to obtain accurate crack stress intensity values, crucial in a thorough crack evaluation. When existing stress intensity solutions are not available, FEA of 3D cracks provides a way to

compute the stress intensity. A method for quickly generating 3D crack meshes within an arbitrary shape

volume is needed to efficiently compute the stress intensity. This method uses a mesh of brick elements todefine the arbitrary shape volume around the crack in the structure. The 3D crack mesh is generated within

the definition mesh and inserted into the larger model; the meshes are connected by bonded contact. For a

crack in a weld, the residual stresses can be included by mapping all stress components from an uncrackedmodel onto the crack mesh as an initial stress. The weld residual stress increases the stress intensity. The

stress intensity is computed using ANSYS results during post-processing.

Introduction

Since all engineering materials contain flaws, such as inclusions, porosity, lack of weld fusion, and pitting,

these defects can cause cracks to form and grow over time in many types of structures. Crack evaluation isimportant in petroleum, chemical, power generation, aerospace, mechanical, and civil structures. A critical

size crack can cause a catastrophic fracture failure, even at low stresses below the yield strength. Using

fracture mechanics methods, a crack can be evaluated using the stress intensity at the crack front todetermine if it is benign or requires repair, and to compute how quickly the crack will grow. Computing

the crack fracture condition and fatigue life allows for an efficient inspection and repair schedule, reducing

risk and cost. Computing the critical crack size also verifies that inspection methods can find the crack while it is still smaller than the critical size to cause fracture.

Accurate crack stress intensity values, K I, are crucial for a thorough crack evaluation. Stress intensitysolutions are available from handbooks and the literature for many basic geometries and crack locations;

however, modeling the actual crack location and orientation in a complicated geometry is an important

improvement for obtaining accurate crack stress intensity values. When an existing stress intensity solutionthat matches the structure geometry and crack location is not readily available, finite element analysis of

3D cracks provides a way to compute the crack front stress intensity. Some of the difficult and time-

consuming tasks to create a 3D crack mesh include generating the collapsed brick elements along the crack

front and the concentric rings of elements around the crack front for the “spider-web” mesh pattern, cracks

following curved surfaces in more complicated geometries, listing the node sets along the crack front

correctly for the J-integral calculation, applying crack plane symmetry constraints, applying crack faceloads, and extracting the J-integral and stress intensity values from the results. When a variety of crack

sizes and locations are examined, the effort to generate each new crack mesh must be repeated. Morecomplicated geometries with numerous possible crack locations prohibit tables of stress intensity values to

be computed for all possible cases; instead the stress intensity needs to be computed for each given crack

location and size. These time consuming modeling difficulties led to the development of FEA-Crack to

generate the 3D crack meshes quickly and easily, and allows cracks at any location to be routinelyanalyzed.

Having an easy-to-use method for quickly generating 3D crack mesh input files within an arbitrary shapevolume is needed to efficiently compute the crack front stress intensity at any location within complicated

structures. This method uses a grid mesh of brick elements extracted from the larger structure model to

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define an arbitrary shape volume with six surfaces around the crack location. The definition mesh volume

has six surfaces to match the shape of the preliminary 3D crack mesh. The 3D crack mesh ANSYS input

file is generated by FEA-Crack within the definition mesh volume and is then inserted back into the larger

model. The meshes can easily be connected by bonded contact in ANSYS [reference 1], which permits a

different mesh pattern between the crack mesh and larger structure mesh.

Welds have regions of tensile residual stresses that increases the crack stress intensity and may adversely

affect the critical fracture condition. When the crack is in or near a weld, the weld residual stresses can beincluded in the crack analysis by mapping all the stress components from the uncracked model residualstress analysis results onto the crack mesh as an initial stress. ANSYS uses an initial stress file [reference

2] to include the residual stresses in a crack analysis along with other boundary conditions. Including both

the weld residual stress and other loading in the crack analysis gives a more thorough and accurate

calculation of the crack front stress intensity.

J-integral Post Processing

After completing the ANSYS analysis, the crack front J-integral and stress intensity values are computed as

an extra post processing calculation using the displacement, stress, and strain results. The J-integral, an

energy release rate, is a preferred method to compute the crack front stress intensity since the calculation isdefined as a contour integral, but can be converted by the divergence theorem to a volume integration

around the crack front. Integration of volume values is a straightforward task using finite element data.Several concentric rings of elements around the crack front allow for comparison of several J-integral

contours to check for acceptable result convergence. The J-integral is computed using element gaussintegration point results in the equation [reference 3]:

1 2

1 1 1

det (1)m

j j j

ij i p j

Volume p crack i k p faces

u x uq J w w q w

x x xσ δ σ

ξ =

∂ ∂ ∂ ∂ = − −

∂ ∂ ∂ ∂ ∑ ∑ ∑

Where m is the number of Gauss integration points in the element, typically 8 in a reduced integration brick element, and w p and w are Gauss integration weighting factors. The summation of the Gauss point p terms

gives the element volume integration. The crack face summation term can be omitted when there are no

tractions on the crack face.

In an elastic analysis, the J-integral values along the crack front can be converted to stress intensity, K I,values using the equation [reference 4]:

( )2(2)

1 I

JE K

ν =

−

Where E is the modulus of elasticity, and ν is the Poisson ratio.

The stress intensity values along the crack front are then available for use in a crack evaluation. As a particular example of a 3D crack in an arbitrary geometry, a set-in nozzle is used to demonstrate the

method.

ExampleAs an example of inserting a 3D crack mesh within a larger and more complicated structure, a pressurevessel with a set-in nozzle and external reinforcing pad is used. The internal surface crack is located at the

shell to nozzle weld, which follows a saddle-shaped 3D surface; see Figure 1.

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Figure 1. Uncracked set-in nozzle mesh

Nozzle Data

For this example, the set-in nozzle dimensions have generic values, which are given as follows. The shellinside radius is 20 in and the shell thickness is 1.5 in. The nozzle inside radius is 10 in, and the nozzle

thickness is 2.0 in. The flange at the top of the nozzle is 2.0 in thick, and has an outside radius of 18 in

from the nozzle centerline. The nozzle length is 20 in above the shell, or a total of 40 in from the shell

centerline to the top of the flange. The shell to nozzle and nozzle to pad welds are 1.5 by 1.5 in. The

reinforcing pad thickness is 1.5 in, and the pad length is 6.0 in from the outside of the nozzle along theoutside surface of the shell; the pad to shell fillet weld is also 1.5 in. The reinforcing pad has a uniform

length as it wraps around the nozzle on top of the shell.

The total crack length, 2c, is 8 in, and the crack depth, a, is 1 in. A large surface crack was used to aid

visualization of the results. In a typical crack assessment a range of small to large crack sizes would beexamined.

An internal pressure of 1000 psi is applied to the inside surfaces of the shell and nozzle. The equivalentaxial pressure thrust is applied to the right end of the shell as a uniform tensile traction of 6425.7 psi. The

top of the nozzle flange is constrained in the vertical direction. Symmetry constraints are applied to the

nodes in the x-y and y-z planes.

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Creating The Analysis Mesh

When building the structure mesh, create a region around the crack location for the definition mesh that

gives the desired shape of the crack mesh. The crack region is left empty in the structure mesh and will be

filled by the crack mesh. For this example the definition mesh volume includes part of the bottom of the

nozzle cylinder and all of the internal nozzle to shell weld. Figure 2 shows the definition mesh beingremoved from the nozzle mesh. The definition mesh, shown in Figure 3, has six surfaces to match the

crack mesh initial shape. The definition mesh brick element shape functions are used directly for the crack mesh shape transformation; more elements in the definition mesh along the curved surfaces give a more

accurate transformed crack mesh shape.

Figure 2. Remove the definition mesh from nozzle mesh

Figure 3. The definition mesh requires a grid pattern of brick elements with 6 surfaces

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To generate the 3D crack mesh, the definition mesh is imported into FEA-Crack from an ANSYS file, and

the crack is located and oriented within the definition mesh. The definition mesh corner node ID numbers

are used as reference points to locate the crack and to select the boundary conditions on each of the six

mesh surfaces. Boundary conditions and contact surfaces are applied to selected surfaces, and the crack

mesh ANSYS input file is created, all within a few minutes. Since the crack mesh is located on the insideof the vessel, the bottom and left surfaces of the crack mesh have the vessel internal pressure applied to

them. The crack faces should also have the internal pressure applied since the crack opens to the inside

surface of the vessel. The top and right surfaces of the crack mesh are selected for bonded contact; theseare the mesh surfaces that connect to the larger vessel mesh. The other two crack mesh surfaces are located

on the two symmetry planes. The front crack mesh face is in the x-y plane and a z-constraint is applied for

symmetry; the back-left crack mesh face is in the y-z plane and an x-constraint is applied for symmetry.The 3D crack mesh is shown in Figure 4 with an offset from the bottom of the nozzle where it is inserted

into the nozzle mesh.

Figure 4. Insert the 3D crack mesh into the nozzle mesh

Without a 3D crack mesh generator and the definition mesh method, the crack mesh modeling tasks would

take many days of effort for a single crack mesh; this crack mesh example was completed in just a few

hours. For this example, the half-symmetric crack is located on the front symmetry plane for easier

visualization; the x-y symmetry plane passes through the center of the crack length leaving the back half of the crack in the final mesh. The surface crack could be located anywhere within the definition mesh andhave other orientations, such as a short radial crack. For cracks at other locations in the nozzle geometry,

another definition mesh can be extracted from the model and replaced with another crack mesh; multiple

cracks could be present in the vessel analysis.

Next, the crack and nozzle meshes are combined within a single ANSYS input file, and bonded contact is

used to connect the two meshes. The element sizes are different along the connected surfaces, especially

near the crack where the mesh refinement in the crack mesh is higher than in the surrounding nozzle and

shell, making bonded contact a useful method to connect the two meshes. The crack mesh generator

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automatically provides the contact surface data on the selected surfaces to aid in combining the mesh input

files. The matching surfaces in the larger mesh must also have the contact surface data defined. In ANSYS

the contact surface is defined by selecting the nodes on each surface. One surface is defined as the target

surface and the other as the contact surface. Of the several available types of contact, bonded contact is

selected using the KEYOPT command so that the two meshes remain connected throughout the analysis.Complete the combining of the two input files by including the internal pressure, equivalent axial pressure

thrust, and symmetry constraints.

Including The Weld Residual Stress

To include the effect of weld residual stress, an uncracked mesh is used to obtain the residual stresses by

applying a thermal strain to only the weld material, as a basic way of simulating the welding process. For a

post-weld-heat-treated structure, the residual stress is typically assumed to be 20% of the yield strength for fracture evaluations. For this example a temperature change of 43.6 oF was imposed on the weld elements

(using a coefficient of thermal expansion of 6.5x10-6 in/in/oF) around the nozzle; the temperature is

unchanged in the rest of the vessel. The stress result components from the uncracked structure results arethen mapped onto the crack mesh as initial stress using the inverse distance weighted (IDW) 3D

interpolation method (Shepard’s method) [reference 5], given by the following equations:

( ) 1, , (3)

n

i i

i F x y z w f

== ∑

1

(4) p

ii n

p

j

j

d w

d

−

−

=

=

∑

( ) ( ) ( )2 2 2

(5)i i i id x x y y z z = − + − + −

Where the value, F ( x, y, z ), is interpolated from the given n data values, f i; for the weld residual stress the f i

values are the stress components from the uncracked analysis, and the F values are the interpolated stress

components applied to the element Gauss integration points in the crack mesh. The wi weighting values are

computed using the distance from the interpolation point position to the surrounding data points. Theexponent value, p, is a positive number, typically 2. A local subset of data points can be used to limit the

stress interpolation to a smaller volume around each interpolation point and speed up the interpolation

calculations. Only elements near the shell to nozzle internal weld will have nonzero initial stress. Theinterpolated residual stresses are included in the ANSYS analysis by referencing the initial stress file from

within the combined input file.

Analysis Results & Discussion

After running the combined crack mesh finite element analysis, the ANSYS results are used to compute thecrack front J-integral and stress intensity during post-processing. Stress results for the whole vessel are

shown in Figure 5, and a close up of the internal surface crack is shown in Figure 6; the displacement scale

is 500 times the actual amount to verify that the crack is opening due to the applied loads. The higher

stress in the nearby welds, due to the residual stress, above the crack can also be seen in Figure 6. A closer zoom-in of the crack depth is shown in Figure 7 (again with 500x displacement), which also gives a better

view of the crack front “spider-web” focused mesh pattern.

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Figure 5. Stress results for internal pressure plus weld residual stress

Figure 6. Stress results, close up of the crack opening, 500x displacement scale

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Figure 7. Stress results, zoom-in at the crack depth, 500x displacement scale

The crack front stress intensity due to the internal pressure with and without the weld residual stress is

compared in the plot in Figure 8 to show how the weld residual stress increases the crack front stressintensity. If the weld is not post weld heat treated, the residual stresses would be much higher, and the

stress intensity would increase even more. To describe the position of the crack front nodes, the plot x-axis

uses the crack phi angle. The crack front phi angle is zero at the crack tip and / 2π at the crack depth, andusing the phi angle allows different size cracks to be compared on the same plot. For this example, the

stress intensity is greatest near the deepest point of the crack (phi of / 2π ), but the position of maximum

stress intensity can change depending on the crack size, crack length-to-depth aspect ratio, crack location,and applied loading. The next step in a crack evaluation is to use the crack front stress intensity values to

determine the critical crack size or compute crack growth rates in a fatigue analysis.

Conclusion

Using a 3D crack mesh generator and the definition mesh method to insert cracks into more complicated

geometries, more accurate crack front stress intensity values can be computed quicker and easier for use in

critical crack size evaluation and fatigue crack growth analysis. Weld residual stress is included in thecrack analysis by interpolating the stress components from an uncracked analysis onto the crack mesh.

Using these two methods makes more thorough and accurate crack evaluations possible by supporting

routine use of 3D finite element crack analysis. An example of a set-in nozzle was used to demonstrate the

3D crack mesh inserted into the nozzle geometry, and the effect of the weld residual stress increasing the

crack front stress intensity.

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Figure 8. Comparison of crack front stress intensity results

References

[1] ANSYS Release 9.0 Documentation, HTML online format, Element Reference, Part I Element Library,CONTA174 and TARGE170 element description.

[2] ANSYS, Commands Reference, I Commands, ISFILE.

[3] T. L. Anderson, Fracture Mechanics, Fundamentals and Applications, 3rd ed., CRC Press, Taylor &

Francis Group, 2005, p. 570.

[4] Anderson, p. 110.

[5] D. Shepard, “A two-dimensional interpolation function for irregularly-spaced data”, Proceedings of the

23rd National Conference ACM, ACM 517-524.

2006 int ansys conf 43

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