STUDY OF FATIGUE CRACK
GROWTH IN 6063-T6 ALUMINUM ALLOY
Nirpesh Vikram
BBDNIIT, Lucknow, India
E-mail: nirpesh.vikram@gmail.com
Raghuvir Kumar
BBDNIIT, Lucknow, India
E-mail: rkg@mnnit.ac.in
Submission: 08/06/2015
Revision: 03/07/2015
Accept: 12/07/2015
ABSTRACT
The
present study relates to investigate the crack propagation behavior of 6063 T6
Al Aluminum Alloy under fatigue loading. The experimental as well as analytical
analysis was done and for crack growth rate for 6063-T6 Aluminum Alloy. All
analysis was done on Side edge notch specimen.
A program was developed on Matlab® to calculate crack growth rate and
effective stress intensity range ratio based on polynomial algorithm. That gave
a very good agreement between them. The effective stress intensity range ratio
(U) was found to depend on stress ratio (R). Variation in load range affects
the crack growth rate. For constant load range its variation was negligible,
constant C was almost constant at variable load range. Variation of maximum
load affects constant C.
Keywords: Fatigue,
6063-T6 Al Alloy, Fracture, Analytical Analysis, Crack Closure
1. INTRODUCTION
The phenomenon of metal fatigue is
very old and is related with mechanical failure of the components subjected to
cyclic loading. Fatigue failure is a major problem encountered by designers.
Generally it occurs in the machine components and structures which are
associated with dynamic loading i.e. the load on a component changing with
time. Although fatigue failure is important in almost all the design problems,
yet the designing of the components of some machines like an aircraft, space
vehicle, turbine, engine, rails & bridges are most critical (BROEK, 1982;
ZHENG, 1983; ELBER, 1970).
According to ASTM (1976) fatigue is
defined as “the process of progressive localized permanent structural change
occurring in the material subjected to the conditions which produce fluctuating
stresses and strain at some point or points and which may culminate in crack or
complete fracture after a sufficient number of fluctuations” (FOREMAN; MEARNEY;
ENGLE ,1967; WALKER, 1970; NIRPESH; RAGHUVIR, 2013; NIRPESH; RAGHUVIR, 2015).
Fatigue failures are generally
caused due to some stress raisers as a crack initiates from these stress raisers.
(PEARSON, 1972; ELBER, 1971; NIRPESH; SAKSHI; RAGHUVIR, 2014) There are three
most important factors which cause the fatigue failure to take place:
·
Cyclic
loading
·
Points
of stress concentration
·
Residual
tensile stresses
2. METHOD
The crack growth rate experiments
have been carried out by various researchers on a wide range of materials using
different specimen geometries (PARIS; ERDOGAN, 1963; BROEK, 1982; ZHENG, 1983;
ELBER, 1970; NICCOLLS, 1976; KUMAR;
GARG, 1988A; KUMAR; GARG, 1988B; ASTM, 1967).
Studies have shown that the crack
propagation is a complex phenomenon. Literature reveals that crack growth rate
(CGR) can be related to ∆K, ∆KƟ etc. these relationships are
empiricalin nature. The CGR constants C, m etc. of different models are
considered to be material constants. In addition to materials they depend upon
loading parameters ∆σ, σm and R.
A number of researchers tried to relate
these constants with the loading parameters for 6061-T6 and 6063-T6 Aluminum
alloys.
Here are the main steps of the work
carried out:
(1)
A
program is written using MAT Lab to calculate the maximum stress intensity
factor Km, stress intensity range ∆K, effective stress intensity
range ∆KƟ and crack growth rate.
(2)
The
program thus developed is used on different sets of data (a-N) for 6061-T6
& 6063-T6 alloys. There is two types of
data:
(a) When maximum load was kept constant
(b) When load range was kept constant
(3)
The
curves are plotted for N Vs a, N Vs, ∆K Vs
and ∆KƟVs
, for both the materials.
(4)
The
constants of the crack growth rate are evaluated for the following models:
(a) Paris and Erdogan model
(b) Elber model
(c) Walker model
(d) Foreman model
(5)
Co-relations
are developed between CGR constants and loading parameters.
3. ANALYSIS
The aim of our study is to see the
effect of loading parameters on the crack growth rate constants. The first
thing is to fit the models in our data and evaluate the constants. It was
planned to analysis models for the given type of loading conditions.
1.
Maximum
load was kept constant and the load ratios were increased.
2.
Load
range was kept constant and load ratios were increased.
3.1.
Materials
used
The material used is 6063-T6 Al
alloys. The chemical composition of the materials as per manufacturer’s
catalogue is given in Table no (1).
Table
1: Chemical
composition of the material
Materials Elements Cu Mg Si Fe Mn Others 6063-T6 Max 0.10 0.90 0.8 0.70 0.60 0.4 Min - 0.40 0.30 - - -
Table
2: Mechanical properties of the materials
Material Properties σy kg/mm2 σu kg/mm2 σf kg/mm2 Ex106 kg/mm2 Elongation % Reduction in area % 6063-T6 14.95 18.26 33.62 5.12 10.7 45.67
3.2.
Fatigue
tests
6063-T6 Al-alloy
1.
Pm
= 820 Kg
2.
ΔP
= 585 Kg
The details of the experiments are
given in Table no (3).
There are 9 experiments in all;
tests S1 – S5 were conducted by keeping maximum load constant. Remaining S6-S9,
were conducted at constant load range.
Fatigue tests were carried out on
the side edged notched specimens of about 180mm x 50mm x 3mm initially with a
notch of 6 mm. During the tests crack initiated from this edge readings of
number of cycles were taken at a regular interval of 0.5 mm crack length.
Table
3
|
Tests for
6063-T6 Al-Alloys |
||||||
|
S.No |
Tests |
R |
Pm Kg |
Pn
Kg |
ΔP Kg |
Nf |
|
1. |
S1 |
0.0 |
820 |
0 |
820 |
61470 |
|
2. |
S2 |
0.2 |
820 |
164 |
656 |
83380 |
|
3. |
S3 |
0.3 |
820 |
246 |
574 |
116000 |
|
4. |
S4 |
0.35 |
820 |
287 |
533 |
137660 |
|
5. |
S5 |
0.45 |
820 |
369 |
541 |
199760 |
|
6. |
S6 |
0 |
585 |
0 |
585 |
479690 |
|
7. |
S7 |
0.2 |
731.25 |
146.25 |
585 |
143030 |
|
8. |
S8 |
0.4 |
975 |
390 |
585 |
96990 |
|
9. |
S9 |
0.6 |
1462.5 |
877.5 |
585 |
76970 |
3.3.
Program
development
A program was developed for
calculating the crack growth rate, maximum stress intensity factor, stress
intensity range and effective stress intensity range, which were later used for
model fitting.
Following data was used as input in
the program, which is written in MATLAB R2012a:
1.
No
of readings of (a-N) in a set Np
2.
Crack
length (a).
3.
Number
of cycles (N)
4.
Maximum
load of the cycle (Pm)
5.
Minimum
load of the cycle (Pn)
6.
Width
of the specimen (w)
First we calculate (R) & (U) (FOREMAN; MEARNEY; ENGLE ,1967; PEARSON,
1972)
(3.1)
(3.2)
To
find out the crack growth rate “seven point successive incremental polynomial
method” was adopted. Following form of equation was formed:
The
general form of the equation is as follows:
(3.3)
The
basic principal to solve these equations is the Gauss elimination method back
substitution is used to solve them. For each set of seven readings values was
found of constants d1-d7 which gave the value of crack
growth rate (da/dN)
(3.4)
After
calculating the first value of crack growth rate, da/dN value was increased
from 0-1 to 2-8 and the above process repeated for second value of da/dN. Thus
calculated the values of da/dN until i=
Np. here Np is the number of reading in a test.
For calculating maximum stress intensity
factor Km, stress intensity range ΔKe (UΔK) following
equations were used:
(3.5)
(3.6)
(3.7)
Where
Output
of the program is given as follows:
1.
Stress
intensity range ratio (U)
2.
Maximum
stress intensity factor (Km).
3.
Stress
intensity range (ΔK).
4.
Effective
stress intensity range (ΔKe)
3.4.
Curves
drawing
Computer program was run for various
test data. From the output curves were drawn. The scheme of the curves is given
below.
(a)
Number
of cycles Vs Crack length
(b)
Number
of cycles Vs crack growth rate.
(c)
Stress
intensity range Vs crack growth rate.
(d)
Effective
stress intensity range Vs crack growth rate.
A. Maximum
load constant
1.
N
Vs a
2.
N
Vs CGR
3.
Log
ΔK Vs log CGR
4.
Log
ΔKeVs log CGR
B. Load
range constant
1.
N
Vs a
2.
N
Vs CGR
3.
Log
ΔK Vs log CGR
4.
Log
ΔKeVs log CGR
3.5.
Model
fitting
3.5.1. Model fitting for 6063- T6 Aluminum alloy:
It is also carried in the two stages
i.e.
(A)
Maximum
load constant
(B)
Load
range constant.
(A)
Maximum
load constant: From Figure
1 and 2 we observed that with increasing load ratios life of components and
crack initiation stage increased while the crack growth rate decreased.
ΔK Vs CGR & ΔKe Vs CGR curves
are drawn for second stage of crack growth rate given by Figure 3 and 4. Lines
of best fit have been drawn, from each set of readings, from which CGR
constants were evaluated for different models as below:
1. Paris model: - A decrement in the value
of constant m is observed. Constant C was found to have a little variation.
2. Elber model: - The values of constant m
were found to be nearly equal to the values of its counterpart in Paris model.
The values of constant C are found to increase if we compare them with that of
the Paris model, which are constant.
3. Walker model: - The values of constant m
have the same variation as it is in Paris and Elber model, but they are
somewhat less in comparison to that of Paris model. The values of constant C
are having very low variation almost negligible. Constant n increased
consistently.
4. Foreman model: - The values of constant
m are equal to the values of constant m in Paris model. Constant C is high in
comparison to the values of C in other models.
(B)
Load
range constant: From Figure 5 and 6 this was observed that with
increasing load ratio life of components & crack initiation stage decreased
while the crack growth rate is found to increase.
ΔK
Vs CGR &ΔKe Vs CGR curves were drawn for second stage of crack growth rate
given by Figure 7 and 8. Lines of best fit have been drawn from each set
readings, from which CGR constants were evaluated of different models as below:
1. Paris model: - Constants m are found to
have very low variations and constant C are found to decrease steadily.
2. Elber model: - In this model the value
of constant m have been found to have very low variation, for analysis purpose
its value may be taken as constant. The value of constant C decreased
consistently.
3. Walker model: - It shows that the value
of constant m has little variation, and is less in comparison to other models.
The constant C was found to decrease continuously. Exponent n has steady
increment.
4. Foreman model: - In this model the value
of constant m is same as that of Paris model. Value of C decreased
consistently, it has higher values in comparison to other models.
3.6.
Relationship
of CGR constants
After
evaluating the crack growth rate constants of different models a relationship
was developed involving constant C and constant m. The constant m is found to
have a relationship with stress range Δσ, constant C bears a relationship with
maximum stress σm. Relationship of C and σm can be
expressed in the form as follows:
(3.8)
Here
&
are
constants which were evaluated by drawing the curve between maximum stress σm
& constant C on semi log scale for each model.
Relationship
between stress range Δσ and constant m is found to be as follows:
(3.9)
Again &
are constants which are evaluated by drawing
the curve between stress range Δσ and constant m on linear scale. Constants T1,
T2, S1 andS2 are given in chapter four.
6063-T6 AL ALLOY
Maximum Load = 820 kg
Crack Length vs Number Cycle
Figure 1: Number of Cycles Vs Crack Length
|
TEST |
S1 |
S2 |
S3 |
S4 |
S5 |
|
R |
0 |
0.2 |
0.3 |
0.35 |
0.45 |
6063-T6 AL ALLOY
Maximum Load = 820 kg
Crack Growth Rate Vs Number of Cycle
Figure 2: Number of Cycles Vs Crack Growth Rate
|
Test |
S1 |
S2 |
S3 |
S4 |
S5 |
|
R |
0 |
0.2 |
0.3 |
0.35 |
0.45 |
6063-T6 AL ALLOY
Maximum Load = 820 kg
Log Crack Growth Rate Vs Log Stress Intensity Range
Figure 3: Stress Intensity range Vs Crack Growth
Rate
|
Test |
S1 |
S2 |
S3 |
S4 |
S5 |
|
R |
0 |
0.2 |
0.3 |
0.35 |
0.45 |
|
U |
.69 |
.79 |
.84 |
.87 |
.93 |
6063-T6 AL ALLOY
Maximum load = 820 kg
Log Ccrack
Growth Rate Vs Log Effective Stress Intensity Range
Figure 4: Effective Stress Intensity range Vs Crack
Growth Rate
|
Test |
S1 |
S2 |
S3 |
S4 |
S5 |
|
R |
0 |
0.2 |
0.3 |
0.35 |
0.45 |
6063-T6 AL ALLOY
Load range = 585 kg
Crack Length Vs Number of Cycle
Figure 5: Number of Cycles Vs Crack Length
|
Test |
S6 |
S7 |
S8 |
S9 |
|
R |
0 |
0.2 |
0.4 |
0.6 |
6063-T6 AL ALLOY
Load Range = 585 kg
Crack Growth Rate Vs Number of Cycle
Figure 6: Number of Cycles Vs Crack Growth Rate
|
TEST |
S6 |
S7 |
S8 |
S9 |
|
R |
0 |
0.2 |
0.4 |
0.6 |
6063-T6 AL ALLOY
Load Range = 585 kg
Log Crack Growth Rate Vs Log Stress Intensity Range
Figure 7: Stress Intensity range Vs Crack Growth Rate
|
Test |
S6 |
S7 |
S8 |
S9 |
|
R |
0 |
0.2 |
0.4 |
0.6 |
6063-T6 AL ALLOY
Load Range = 585 kg
Log Crack
Growth Rate Vs Log Effectivestress Intensity
Range
Figure 8: Effective Stress
Intensity range Vs Crack Growth Rate
|
Test |
S6 |
S7 |
S8 |
S9 |
|
R |
0 |
0.2 |
0.4 |
0.6 |
|
U |
.69 |
.79 |
.90 |
1.03 |
4. RESULTS & DISCUSSION
To evaluate constants C & m the
maximum stress Vs log C and stress range Vs m curves were used.
Constant C was plotted on log scale
with maximum stress on linear scale. Slopes & intercepts give constants respectively. Straight line passing through
maximum number of points has been drawn for each model. Slope of the lines
gives constant T1& intercepts of the lines gives constant T2.
The constants evaluated are given in Table no (4) for different models.
Table
no 4: Constants for 6063-T6 Al Alloy
|
Model |
|
|
||
|
Constant
S1 |
Constant
S2 |
Constant
T1 |
Constant
T2 |
|
|
Paris |
3.70 |
30.85 |
-3.25 |
6.49 |
|
Elber |
2.95 |
21.89 |
-3.46 |
7.19 |
|
Walker |
3.11 |
25.29 |
-2.08 |
1.68 |
|
Foreman |
4.18 |
6.66 |
-3.25 |
6.49 |
5. CONCLUSIONS
Variation in load range affects the
crack growth rate constant m, i.e. constant m had the higher variation when
load range was varying. For constant load range its variation was negligible
constant C was almost constant at variable load range.
Variation of maximum load affects
constant C, i.e. constant C in found to vary with maximum load. At constant
maximum load it is found to be almost constant.
Walker
model modifies the constants m of Paris model, by introducing a new constant n.
This constant n is the exponent of maximum stress intensity Km
modification introduced in constant C is negligible.
Foreman
model modifies the constant C of Paris model by introducing the fracture toughness
Kf of the material. It does not affect constant m.
Elber
model introduces a slight modification in Paris model for both constants C
& m.
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