Fracture Mechanics in Engineering Structures
Fracture of Divertor Structures
Jake Blanchard
ARIES Meeting
April 2011
Outline
Primer on Fracture Mechanics
Preliminary Results for Divertor
Structures
Future Plans
Design of Engineering Structures
In early 20
th
century, design of metal
structures was strictly stress based
Onset of high performance ships (Liberty
ships, WWII) changed things
What happened?
stress
Temperature
fracture
Low strength
high strength
Fracture Mechanics
Size and Orientation of Cracks
Stress Fields
Material Properties
Crack Tip Stress Fields (Elastic)
Consider a sharp crack in an elastic
material
K is stress intensity factor
Function of geometry and
loading
Fracture occurs when K
reaches critical value (K
IC
–
fracture toughness)
r
An Example
Consider an infinite plate with a through
crack
Glass: K
IC
=1
MPa-m
0.5
Al:
K
IC
=20 MPa-m
0.5
For a=100 microns,
fracture stresses are 56
MPa for glass and 1,100
MPa for Al
Fracture Toughness (room temp)
These values depend strongly on processing.
Ductile vs. Brittle
Temperature Dependence
Stress Fields in Ductile Materials
Ductile materials will develop plastic
deformation at crack tips
This toughens material and resists
catastrophic crack growth
Previous analysis is not valid
Analysis uses integral around crack
tip, rather than stress intensity factor
Failure Criterion for Ductile
Materials
Base failure prediction
on work required to
create fresh fracture
surface
Write as line integral
W=strain energy density
T=tractions
U=displacement
Irradiated Materials
Fatigue Crack Growth
Previous analyses refer to catastrophic,
unstable crack growth
Repeated application of loads can lead to
incremental crack growth
Characterizing Cracks
Key Question: What is initial crack size?
We need non-destructive examination
(NDE)
Options:
◦
Dye penetrant
◦
Ultrasound
◦
X-rays
◦
Eddy currents
◦
Thermography
◦
Etc.
Costs and capabilities vary
ITER Structural Design Criteria
Primary Loads
Primary + Secondary Loads
Elasto-Plastic Analysis
A
N
S
Y
S
F
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t
e
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m
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n
t
M
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f
C
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a
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C
r
a
c
k
Crack face
•
Stress intensities along crack face using the ANSYS CINT command
•
Elastic-Plastic material properties for Tungsten used
•
Currently only pressure loads are considered, but thermal stresses to be included
Initial Fracture Studies Based on T-Tube
Geometry and Pressure Loads
Initial Studies Compute Stress
Intensities for Axial Cracks in
Pressurized Cylinder
Case 1: Circular crack; c/a=1
Case 2: Elliptical crack; c/a=2
Use elastic-plastic properties
for tungsten.
Calculate J
1
and then report
equivalent K
I
.
Variation of Stress Intensity with Location
along Crack Tip (a = 0.1 mm)
Case 1: Circular crack; c/a=1
Case 2: Elliptical crack; c/a=2
a = 0.1mm
Maximum Stress Intensity as a
Function of Crack Depth
Conclusions
We’ve got to include fracture in our
design analysis, particularly when using
materials with limited ductility
So far, there are no major red flags
We will include thermal stresses in the
future
Explore the world of fracture mechanics in engineering structures, encompassing the importance of stress fields, crack tip behaviors, fracture toughness, ductile versus brittle materials, and the influence of temperature dependence on material properties. Delve into the intricacies of crack initiation and propagation, stress intensity factors, and the critical values governing fracture occurrences in different materials. Gain insights into how these principles shape the design and analysis of engineering components to ensure structural integrity and safety.
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Presentation Transcript
Fracture of Divertor Structures Jake Blanchard ARIES Meeting April 2011
Outline Primer on Fracture Mechanics Preliminary Results for Divertor Structures Future Plans
Design of Engineering Structures In early 20thcentury, design of metal structures was strictly stress based Onset of high performance ships (Liberty ships, WWII) changed things
What happened? high strength stress fracture Low strength Temperature
Fracture Mechanics Size and Orientation of Cracks Stress Fields Material Properties
Crack Tip Stress Fields (Elastic) Consider a sharp crack in an elastic material r K is stress intensity factor Function of geometry and loading Fracture occurs when K reaches critical value (KIC fracture toughness)
An Example Consider an infinite plate with a through crack K I = = a K IC K = IC allow a Glass: KIC=1 MPa-m0.5 Al: KIC=20 MPa-m0.5 For a=100 microns, fracture stresses are 56 MPa for glass and 1,100 MPa for Al
Fracture Toughness (room temp) Material 7075 Aluminum 4340 Steel Silicon Carbide Polystyrene Tungsten (polycrystalline) Beryllium Toughness (MPa m^0.5) 24 50 4 1 5 10 These values depend strongly on processing.
Stress Fields in Ductile Materials Ductile materials will develop plastic deformation at crack tips This toughens material and resists catastrophic crack growth Previous analysis is not valid Analysis uses integral around crack tip, rather than stress intensity factor
Failure Criterion for Ductile Materials Base failure prediction on work required to create fresh fracture surface Write as line integral u = J Wdx t ds W=strain energy density T=tractions U=displacement 2 I x 1 1 2 = 2 J K IC IC 3 E
Fatigue Crack Growth Previous analyses refer to catastrophic, unstable crack growth Repeated application of loads can lead to incremental crack growth
Characterizing Cracks Key Question: What is initial crack size? We need non-destructive examination (NDE) Options: Dye penetrant Ultrasound X-rays Eddy currents Thermography Etc. Costs and capabilities vary
ITER Structural Design Criteria Primary Loads . 0 33 K K I C Primary + Secondary Loads . 0 67 K K I C Elasto-Plastic Analysis . 0 67 J J I C
ANSYS Finite Element Model of Circumferential Crack Stress intensities along crack face using the ANSYS CINT command Elastic-Plastic material properties for Tungsten used Currently only pressure loads are considered, but thermal stresses to be included Crack face
Initial Fracture Studies Based on T -Tube Geometry and Pressure Loads Tungsten OD = 15 mm Coolant pressure ~ 10 Mpa Coolant inlet temperature ~ 600 oC t = 1 mm
Initial Studies Compute Stress Intensities for Axial Cracks in Pressurized Cylinder Case 1: Circular crack; c/a=1 Case 2: Elliptical crack; c/a=2 Use elastic-plastic properties for tungsten. Calculate J1 and then report equivalent KI.
Variation of Stress Intensity with Location along Crack Tip (a = 0.1 mm) 1.3 cylindrical 1.2 elliptical K1 (MPa-m1/2) 1.1 1 0.9 Case 1: Circular crack; c/a=1 0.8 0 15 30 45 60 75 90 Case 2: Elliptical crack; c/a=2 (degrees) a = 0.1mm
Maximum Stress Intensity as a Function of Crack Depth 3.5 3 2.5 K1 (MPa-m1/2) 2 1.5 Cylindrical 1 Elliptical 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Crack Depth (mm)
Conclusions We ve got to include fracture in our design analysis, particularly when using materials with limited ductility So far, there are no major red flags We will include thermal stresses in the future
