May 19, 2014

SSC Ship Structures Symposium 2014

Maritime Institute of Technology & Graduate Studies, Linthicum Heights, Maryland

XFA3D Toolkit for Fatigue Damage Assessment of Welded

Aluminum Structures under Variables Amplitude Loading

Jim Lua1, Eugene Fang1, Xiaohu Liu1, Alireza Sadeghirad1

David Chopp2

1

1Global Engineering and Materials, Inc. (GEM)

1 Airport Place, Suite 1

Princeton, NJ

2Dept. of Engineering Science

and Applied Mathematics

Northwestern University

Evanston, IL

OUTLINE

DoD relevance and problem challenges

Objectives

XFA3D toolkit overview

XFA3D theory background

Simplified residual stress characterization

approach

Capability demo

without residual stress

with residual stress

Summary and future study

DoD Relevance (Metallic)

• Immediate Needs

– a verified computational tool to efficiently

perform

• Structural integrity and residual strength

assessment;

• Durability assessment for a given cyclic

loading; and

• Reliability based performance evaluation

with in-service structural health monitoring

– a high-fidelity virtual testing tool to address

• What is the critical damage size at onset

and growth phase ?

• When should the structure be repaired ?

• Is the damage critical to the structure ?

• What are the residual strength and design

allowables under cyclic loading ?

Helicopter

Component

SSC-435

MAHI

Technical Challenges

Lack of test data

• Material and Structural performance

data under multiaxial fatigue

Damage tolerance (DT) and fail safe (FS)

approaches

• Initial inspection and re-inspection (DT)

• Inspectability (DT)

• Costly and lengthy downtime for

repairs (FS)

Complicated crack path and geometry

• Use of adaptive remeshing

• Use of mesh independent approach

(XFEM)

Adaptive remeshing

XFEM

Objectives

– Develop, demonstrate, and validate the

capability of XFA3D for metallic fatigue analysis

– Create an efficient XFEM-based modeling

approach to allow for performance evaluation

and structural integrity assessment with in-

service structural healthy monitoring. Assist in

risk informed decision making on repair,

maintenance, and life extension options.

• A toolkit for simulation of mesh-independent 3D fatigue

crack growth based on XFEM technology and

Abaqus/Standard solver

• Development status

– Ongoing support from US government agencies

– Trial versions being tested by users at US Navy

What is XFA3D?

Key Technology: XFEM

Representation of a general

crack

Lset for

Crack Surface (f)

Lset for

Crack Front (Y)

Regular Elements

Initial Crack

Continuous displacement Jump enrichment at crack wake

Tip enrichment

Key Technology: 3D Crack Tracking

Narrow-Band

Fast Marching Method

(FMM)

One-Step Solution for Residual Stress

Characterization

• Motivation

– capture the effects of residual stress without requiring two separate

analyses in each increment of crack propagation.

• Main assumption

– the ratio of contributions of the residual stress and external loading is

constant during the simulation.

• Summary of algorithm

a) compute ratio a from two preliminary simulations by considering 1) only the

maximum loading and 2) only the residual stress.

b) modify R ratio in each increment of the fatigue crack propagation

simulation:

max max

.res initial res

load initial load

K Kconst

K Ka

0min min

max max 1

load res

load res

RK K KR

K K K

a

a

Numerical Implementation within

XFA3D Toolkit

Simulation under

external loading at the

initial configuration

Simulation under

residual stress at the

initial configuration

max

initial loadK

initial resK

max

initial res

initial load

K

Ka

R-ratio dependent

fatigue crack

propagation model max max

min min

max min max min 0 max

0min min

max max

(1 )

1

load res

load res

load load load

load res

load res

K K K

K K K

K K K K K R K

RK K KR

K K K

a

a

At each increment:

Summary of R-Ratio Dependent

Fatigue Models

• Walker’s Model:

• NASGRO’s Model:

1

m

da KC

dN R

max

11

11

p

thn

p

crit

K

da f KC K

dN R K

K

: Walker’s constant

for the material

ΔKth : threshold stress intensity range

Kc : critical stress intensity factor

C, n, p and q: empirically derived

f: crack tip opening function

a: plain stress/strain constraint factor

: ratio of the maximum applied

stress to the flow stress

2 3

0 1 2 3

0 1

0 1

max , , 0

, -2 0

2 , 2

R A A R A R A R R

f A A R R

A A R

1/

2 max0

0

max1

0

2 0 1 3

3 0 1

(0.825 0.34 0.05 ) cos2

(0.415 0.071 )

1

2 1

SA

S

SA

S

A A A A

A A A

a

a a

a

max 0/S S

Structure

Mesh

Loads/BC

Material

Abaqus/CAE

XFA3D Model

Fatigue Law

XFEM Parameters

XFA3D user interface

Base Model

XFA3D Parameters

XFA3D model

Crack

Crack Surface

Crack Front

Abaqus/CAE

A Holed Plate with an Initial Crack

200 x 50 x 5mm plate with hole r = 10 mm

Applied peak far field stress = 20.8 MPa

Load ratio = 0.1

Aluminum material

E = 71.2 GPa

n= 0.33

C = 2.2e-10

m = 3.545

Initial crack at 45° angle, initial length = 2 mm

Boljanović, S., Maksimović, “Analysis of the crack growth propagation process under mixed-mode loading,”

Engineering Fracture Mechanics, 78, 1565-1576, 2011.

XFA3D Model for the Holed Plate

Global model with

XFA3D zone XFA3D zone mesh with initial crack

surface (mesh independent)

Total number of elements = 46568

Number of XFA3D elements = 17964

Initial Response without Growth

Unit: MPa

Deformation

magnified

KI = 0.90 MPa mm^0.5

KII = 0.09 MPa mm^0.5

KIII ~= 0

Crack Growth Movie (Holed Plate)

Verification of Crack Path and K(a)

Prediction

Edge-cracked Beam Subject to Three Point

Bending

Peak load = 5000 N

Load ratio = 0.1 Polymethyl Methacrylate Material (PMMA)

E = 3.3 GPa

n = 0.38

C = 2.0 e-3

m = 6.46

Boljanović, S., Maksimović, “Analysis of the crack growth propagation process under mixed-

mode loading,” Engineering Fracture Mechanics, 78, 1565-1576, 2011.

XFA3D Model and Its Initial Response for

Holed Beam with an Initial Crack

Total number of elements = 23128

Number of XFA3D elements = 5884

KI = 1.17 MPa mm^0.5

KII = 0.11 MPa mm^0.5

KIII ~= 0

Crack Growth Movie (Holed Beam )

Display of Cracked

Surface

Verification of Crack Path

Prediction

Fatigue Damage Characterization under

Blocking Loading

• Parameters to define the block loading

Verification Examples for Fatigue

Crack Growth in Welded Component

• Butt Welded Tensile Specimen

• Cruciform Tensile Specimen

• Welded T-Joint

Butt welded tensile specimen

welded 2024-T351 aluminum alloy

Use of NASGRO fatigue equation

Initial residual stress

measurement in the butt welded

tensile example. The red line is

the approximated residual stress

profile introduced to XFA3D.

Liljedahl C.D.M., Zanellato O., Fitzpatrick M.E., Lin J., Edwards L., “The effect of weld residual stresses and their re-distribution with crack

growth during fatigue under constant amplitude loading”, International Journal of Fatigue 32, 735–743, 2010.

XFA3D Model

NASGRO fatigue equation with the material constants, available in

DOT/FAA/AR-05/15, Office of Aviation Research, 2005.

Maximum applied load = 33.71 kN

Load ratio = 0.1

Modulus of elasticity =72 GPa

Poisson’s ratio = 0.33.

Residual Stress and K Solution for

an Initial Crack

277.24 =1.67

165.91

initial res

initial load

K

Ka

Effects of Residual Stress on Crack

Growth

a = 10.7 mm a = 26.7 mm a = 46.8 mm

Cruciform Tensile Specimen with a Semi-

Elliptical Surface Crack

6061-T651 aluminum

Walker’s fatigue equation

0.33n

0.641

3.7m

10000E kips

C = 1.17 x 10-9

Summary of XFA3D Model with an

Initial Crack

Initial Residual Stress Definition and

Calculation

0.158initial res

initial load

K

Ka

Evolution of 3D Crack Front

Effects of Tensile Residual Stress

Number of cycles versus increment numbers obtained from the

simulations with and without considering the residual stress.

Welded T-joint with a through-the-

thickness Crack

0.3n

200E GPa

0.0

3.0m

C= 4.75 x 10-12

XFA3D Model and Initial Crack

Location

Initial Residual Stress Definition and

Calculation

0.077initial res

initial load

K

Ka

Crack Propagation in T-Joint (Movie)

Comparison of a(N) Curves

under Constant Amplitude Loading

Comparison of a(N) Curves

under Block Loading

Summary and Conclusions

• Developed a simplified residual stress characterization

model based on a single-step solution

• Demonstrated and verified its applicability for small

component with a dominant tensile residual stress field

• Demonstrated XFA3D toolkit for

– mesh independent crack insertion and growth

prediction

– characterization of the interaction between the crack

growth and the associated complex geometry

– characterization of fatigue damage accumulation

under a block loading spectrum

Future Work

• Capability exploration of XFA3D for a large welded

structure with a combined tensile and compressive

residual stress

• Advanced fatigue damage accumulation model

under

– near tip plasticity

– multiaxial loading

• Extension of XFEM element library for high order

tetrahedral element to characterize a complex 3D

structure

Acknowledgments

This work is supported by Office of Naval

Research (ONR) 331 under contract N00014-13-

C-0108 with Dr. Paul Hess as the program

monitor.

Authors would like to thank Yared Amanuel at

NSWCCD for providing his verification resdults of

XFA3D and suggestions on its capability

extension.