Stress Intensity Factors for Three-Dimensional Cracks in Plates Subjected to Thermal and Displacement Controlled Loading M. Uslu 1 , C. Kurtis 1 , A. O. Ayhan 2,* , E. Nart 3 1 Sakarya University, Mechanical Eng. Dept., Sakarya, TURKEY 2 Yildiz Technical University, Mechanical Eng. Dept., Istanbul, TURKEY 3 Sakarya University, Mechatronics Eng. Dept., Sakarya, TURKEY * [email protected]
CFRAC2011_FCPAS
Aug 26, 2014
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Stress Intensity Factors for Three-Dimensional
Cracks in Plates Subjected to Thermal and
Displacement Controlled Loading
M. Uslu1, C. Kurtis1, A. O. Ayhan2,*, E. Nart3
1Sakarya University, Mechanical Eng. Dept., Sakarya, TURKEY
2Yildiz Technical University, Mechanical Eng. Dept., Istanbul, TURKEY
3Sakarya University, Mechatronics Eng. Dept., Sakarya, TURKEY
Outline
�Displacement–Controlled Loading
�Problems Studied
�Analysis Method
� FCPAS – Fracture and Crack Propagation Analysis System
� Enriched Finite Elements
� Finite Element Models
�Stress Intensity Factors
�Uniform Far-Field Stress & Displacement Loads (UFFS & D)
�Bending Far-Field Stress & Displacement Loads (BFFS & D)
�Crack Growth Simulations
�Uniform Far-Field Stress & Displacement Loads (UFFS & D)
�Bending Far-Field Stress & Displacement Loads (BFFS & D)
�Summary and Conclusions2
Thermal and Displacement Controlled Loads
3
(D. Peterson, Sandia
Nat. Lab. 1998)
(Ayhan and Nied, 1997)
(W. Moussa, Univ. of Alberta
Website)
(ANSYS User Group Pres..
2001, PennState Un. Website)
(NASA Website)
Load-Controlled Loading
4
a
K
Increasing Stress Intensity Factor and Crack
Growth Rate with Increasing Crack Length
σo
σo
Displacement-Controlled Loading
5
a
K
Stress Intensity Factor Decreases with Increasing
Crack Length - Cracks May Arrest Under
Displacement & Thermal Loading Conditions
Dd
Dd
6
Uncracked
Model
Insert Crack
and Re-mesh
Model
Apply B.C.’s
Analyze
Cracked Model
(FRAC3D)
Post-Process,
Check Failure
Predict Next
Crack Profile
Insert/Grow
New Crack
Re-mesh New
Cracked Model
Failed?
STOP
CALCULATE LIFE
Y
N
FCP
AS
GU
I
FCPAS GUI
FCP
AS
GU
I
FCPAS GUI
FCPAS - Fracture and Crack Propagation Analysis System(http://www.yildiz.edu.tr/~aoayhan/FCPAS/index.htm)
7
−+
−+=
∑∑
∑∑∑
==
===
nodel
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ntip
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nodel
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11
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11
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),,(),,()(),,(),,(),,(
ρηξρηξξρηξ
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==
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Unknown Stress Intensity Factors Are Included in the FE Formulation & Solved for Directly
3D Enriched Finite Elements
FRAC3D – FCPAS Solver for 3D Fracture Analysis
8
Supported Element Types
ξξξξ
ηηηη
ρρρρ
ξξξξ
ηηηη
ρρρρ
ξξξξ
ηηηη
ρρρρ
ξξξξ
ηηηη
ρρρρ
32-Node Hexahedron
20-Node Hexahedron
26-Node Pentahedron
10-Node Tetrahedron
ξξξξ
ηηηη
ρρρρ
15-Node Pentahedron
Boundary Conditions
FRAC3D – FCPAS Solver for 3D Fracture Analysis
9
• Load Types
– Pressure Loading on Surfaces
– Concentrated Forces on Nodes
– Thermal Loading
– Inertia Loading
– Centrifugal Loading
• Constraints
– Displacement Constraints on
Nodes
– Constraints on Node Sets (Tied
Nodes)
– Displacements on Skew Edges
– Sub-model BC’s from ANSYS
Analysis Types & Material Systems Supported
10
• Analysis Types
– Elastic Stress Analysis
– Elastic/Plastic Stress Analysis
– Linear Elastic Fracture Mechanics w/ & w/o plasticity on uncracked material
– Submodeling of ANSYS models
• Material Systems
– Homogeneous Isotropic
– Bi-material Isotropic
– Homogeneous Orthotropic
– FGM Isotropic
– Elastic/plastic Isotropic
FRAC3D – FCPAS Solver for 3D Fracture Analysis
Surface Cracks in Plates – Uniform Loads
11
Uniform Far Field Stress Loading (UFFS)
(Load Controlled Conditions)
Uniform Far Field Displacement Loading (UFFD)
(Displacement Controlled Conditions)
Finite Element Models
12
General View Crack Region Close-up View
Structured Mesh Near Crack Front, Unstructured Mesh Elsewhere
Surface Cracks in Plates - Validation
13
Uniform Far Field Stress Loading
(UFFS)
(a/c=0.2, a/t=0.2, 0.6)
2c
aθθθθ
Uniform Far Field Stress Loading
(UFFS)(a/c=1.0, a/t=0.2, 0.6)
2c
aθθθθ
FCPAS Predictions Agree Well with Those of Newman and Raju
Thermal and Displacement Loads
14
Uniform Far Field Displacement Loading (UFFD)
Uniform Temperature Change with Fixed Ends (UTCFE)
(a/c=0.2, a/t= 0.4)
Normalized SIFs are Same for UFFD and UTCFE Loads
Comparisons of UFFS and UTCFE Loads
15
(a/c=1.0, a/t=0.2, 0.4)
2c
aθθθθ
Small Differences Along Crack Front Between UFFS and UTCFE for
Small Crack Sizes
Comparisons of UFFS and UTCFE Loads
16
(a/c=1.0, a/t=0.6, 0.8)
2c
aθθθθ
Higher Differences Along Crack Front between UFFS and UTCFE for
Larger Crack Sizes
Surface Cracks in Plates – Bending Loads
17
Bending Far Field Stress Loading (BFFS)
(Load Controlled Conditions)
Bending Far Field Displacement Loading (BFFD)
(Displacement Controlled Conditions)
Thermal and Displacement Loads
18
Bending Far Field Displacement Loading (BFFD)
Bending Temperature Change with Fixed Ends (BTCFE)
(a/c=0.2, a/t= 0.4)
Normalized SIFs are Same for BFFD and BTCFE Loads
2c
aθθθθ
Comparisons of BFFS and BTCFE Loads
19
(a/c=1.0, a/t=0.2, 0.4)
2c
aθθθθ
Near-Surface Differences Between BFFS and BTCFE
Comparisons of BFFS and BTCFE Loads
20
(a/c=1.0, a/t=0.6, 0.8)
2c
aθθθθ
Higher Near-Surface Differences Between BFFS and BTCFE for Larger Crack
Sizes
Simulation of Crack Growth – Validation
21
Cra
ck L
ength
(mm
)
Number of Cycles
Experiment(Reytier, M., 2004)* Crack Profiles by FCPAS
FCPAS
FCPAS Simulation Results Agree Very Well with Experimental Observations*(The permission by OMMI (Power Plant: Operation Maintenance and Materials Issues) and its publisher European Technology
Development Ltd. UK, for reproducing and republishing data by Reytier, M. is gratefully acknowledged.)
Surface Crack in a Finite-Thickness
Plate under Bending Load
Simulation of Crack Growth – UFSS & UFFD
22
UFFS Load
a0/c0=1
a0/t=0.1
Crack Advancement Profiles Nearly Same for UFFS and UFFD Loads
UFFD Load
a0/c0=1
a0/t=0.1
da/dN=C(∆K)n
[m/cycle=C(MPa(m)0.5)n]
C=7.1E-10
n=3
23
Dimensional Stress Intensity Factor vs. Crack Depth Length
Higher SIF Differences as Crack Advances
a0/c0=1
a0/t=0.1
Simulation of Crack Growth – UFSS & UFFD
24
Normalized Crack Depth Length vs. Number of Load Cycles
Higher Crack Growth Life Predicted for UFFD Loads
a0/c0=1
a0/t=0.1
da/dN=C(∆K)n
C=7.1E-10
n=3
Simulation of Crack Growth – UFSS & UFFD
Simulation of Crack Growth – BFSS & BFFD
25
BFFS Load
a0/c0=1
a0/t=0.1
Higher Growing Crack Aspect Ratio for BFFD Loads
BFFD Load
a0/c0=1
a0/t=0.1
da/dN=C(∆K)n
C=7.1E-10
n=3
26
Dimensional Stress Intensity Factor vs. Crack Depth Length
Higher SIF Differences as Crack Advances
a0/c0=1
a0/t=0.1
Simulation of Crack Growth – BFSS & BFFD
27
Normalized Crack Depth Length vs. Number of Load Cycles
Higher Crack Growth Life Predicted for UFFD Loads
a0/c0=1
a0/t=0.1
da/dN=C(∆K)n
C=7.1E-10
n=3
Simulation of Crack Growth – BFSS & BFFD
Surface Cracks in Cylindrical Rods
28
Stress Load Displacement Load
Un
ifo
rmB
en
din
g
Crack Growth Profiles Similar – Similar SIF Distributions Along Crack Front
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000
Number of Cycles
Stress Load, a/c=1.0
Displacement Load, a/c=1.00.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000
Cra
ck L
eng
th(a
)
Number of Cycles
Stress Load, a/c=1.0
Displacement Load, a/c=1.0
Surface Cracks in Cylindrical Rods
29
UFFS & UFFD
Crack Growth Life Predictions
Significant Crack Growth Life Differences Even up-to a/D=0.5
BFFS & BFFD
da/dN=C(∆K)n
C=7.1E-10
n=3
Summary and Conclusions
30
� Displacement-controlled and thermal loading conditions are often encountered in real-life
engineering applications.
� Enriched finite elements allow computation of SIFs and simulation of crack growth in three-
dimensional structures accurately and efficiently
�No special mesh and post-processing needed
�FCPAS (Fracture and Crack Propagation Analysis System) – currently automated crack growth
simulations in plates and cylinders under different loading and boundary conditions
� Uniform stress and displacement loads on plates with surface cracks
�Crack growth profiles (a/c ratios) nearly same for growing crack
�Crack growth life higher for displacement/thermally loaded plates
� Bending stress and displacement loads on plates with surface cracks
�Crack growth profiles (a/c ratios) gets smaller under displacement loads as crack grows
�Crack growth life higher for displacement/thermally loaded plates
� Non-dimensional stress intensity factors the same along crack fronts for displacement loads the thermal
loads with plate fixed ends
Acknowledgements
31
�Authors are thankful to The Scientific and
Technological Research Council of Turkey
(TUBITAK) for the financial support and to the
administration and personnel of Çukurova, Sakarya
and Yildiz Technical Universities for the
organizational support.
�Authors are thankful to The Scientific and
Technological Research Council of Turkey
(TUBITAK) for the financial support and to the
administration and personnel of Çukurova, Sakarya
and Yildiz Technical Universities for the
organizational support.