Figure X – name
Figure 1 – Hardness Measurement Locations
Experimental Data:
Table 1 – Experimental Hardness Data for Straight Weld (Rockwell E Scale)
Flat (1)
Flat (2)
Beveled (1)
Beveled (2)
"-1in."
98.05
99.75
99.10
100.50
"-1/2in."
101.75
100.00
101.00
104.15
Straight Weld
"-1/4in."
"0in."
"1/4in."
103.00
99.65
100.75
103.90
99.60
105.50
100.70
101.00
99.90
102.75
102.50
103.50
"1/2in."
100.00
99.00
101.25
105.75
"1in."
101.75
101.00
100.05
100.75
Table 2 – Experimental Hardness Data for Diagonal Weld (Rockwell E Scale)
Flat (1)
Flat (2)
Beveled (1)
Beveled (2)
"-1in."
99.55
101.35
100.00
95.40
"-1/2in."
103.00
106.25
105.75
101.75
Diagonal Weld
"-1/4in."
"0in."
"1/4in."
103.50
102.90
104.60
104.00
103.00
106.00
105.25
101.50
103.45
102.60
102.50
102.50
"1/2in."
104.10
103.00
102.75
102.00
"1in."
101.25
101.00
101.75
101.10
Table 3 – Ultimate Tensile Strength (psi)
Factor 1
A:Weld Angle
Straight
Straight
Diagonal
Diagonal
Straight
Straight
Diagonal
Diagonal
Factor 2
Response 1
B:Joint Type UTS (psi)
Flat Butt
44000
Flat Butt
60000
Flat Butt
44000
Flat Butt
48000
Beveled Butt
56000
Beveled Butt
80000
Beveled Butt
64000
Beveled Butt
56000
Tables 1 and 2 display the Rockwell Hardness values for both flat and beveled joints for the
straight and diagonal welds, respectively. Hardness values were measured at locations shown in Fig.1.
Table 3 shows the ultimate tensile strength (UTS) for varying combinations of weld angle and joint
type. Each measurement had two replicates in order to analyze an average set of values for the
measurements.
Results and Interpretation:
Table 4 – Analysis of Variance for Ultimate Tensile Strength
Source
Model
A
B
AB
Pure Error
Cor Total
Sum of Squares DF Mean Square
550000000 3 183333333.3
98000000 1
98000000
450000000 1
450000000
2000000 1
2000000
456000000 4
114000000
1006000000 7
F Value
1.608187135
0.859649123
3.947368421
0.01754386
Prob > F
0.3209
0.4063
0.1179
0.9010
not significant
not significant
not significant
not significant
An Analysis of Variance, or ANOVA, for ultimate tensile strength is shown in Table 4. The
value given in the “Prob>F” column determines whether or not a given factor has a significant effect
on the dependent variable. If this value is less than 0.05, then the factor has a significant effect. If this
value is greater than 0.10, then there is no significant effect. Since the “Prob>F” values given in Table
4 are all greater than 0.05, is can be said that neither the weld angle, joint type, nor the interaction
between them have significant effects on the ultimate tensile strength of the specimens.
Figure 2 – Main Effect Plots for Weld Angle (left) and Joint Type (right) on UTS
The main effect plots shown in Fig.2 display the effects that a change in weld angle or joint
type have on the ultimate tensile strength of the specimen. Changing from a straight weld to a
diagonal weld, for the flat butt joint in Fig.2, results in a decrease in UTS from 52,000 psi to 46,000
psi. This difference of 6,000 psi is minimal, considering the possible inconsistencies in welds.
Changing from a flat butt joint to a beveled butt joint, for the straight weld in Fig.2, results in an
increase in UTS from 52,000 psi to 68,000 psi. Again, this difference is still considered insignificant.
Figure 3 – Interaction Effect Plot of Weld Angle and Joint Type on UTS
The interaction plot for the effect of weld angle and joint type on the ultimate tensile strength is
shown in Fig.3. Since there is no intersection, there is no interaction effect. This agrees with the
ANOVA Table (Table 4).
Figure 4 – Normal Plot of Residuals for Ultimate Tensile Strength
The normal plot shown in Fig.4 is for the ultimate tensile strength. Because the points in Fig.4
lie along the fit line without deviating too far, it is safe to assume that the data is normally distributed
and that the collected data is reliable.
Table 5 – Analysis of Variance for Hardness
Source
Model
A
B
C
AB
AC
BC
ABC
Pure Error
Cor Total
Sum of Squares
181.2285714
22.12571429
0.642857143
102.5948214
10.63142857
10.19803571
14.54964286
20.48607143
73.645
254.8735714
DF
27
1
1
6
1
6
6
6
28
55
Mean Square
6.712169312
22.12571429
0.642857143
17.0991369
10.63142857
1.699672619
2.424940476
3.414345238
2.630178571
F Value
2.551982358
8.412247946
0.244415778
6.501131555
4.042093829
0.646219476
0.921968
1.298141987
Prob > F
0.0082
0.0072
0.6249
0.0002
0.0541
0.6926
0.4942
0.2904
significant
significant
not significant
significant
not significant
not significant
not significant
not significant
Table 5 shows the ANOVA for casting porosity. Again, if the “Prob>F” is less than 0.05, there is
a significant effect. Since factor A, the weld angle, has a “Prob>F” value less than 0.05, it can be said that
the angle of the weld has a significant effect on the hardness of the specimen. Also, it can be seen that
factor C, the location of the hardness measurement, has a significant effect on the hardness of the
specimen. The interactions between weld angle, joint type, and location of hardness measurement do not
seem to affect the hardness of the specimen.
Figure 5 – Main Effect Plots for Weld Angle (left) and Joint Type (right) on Hardness
The main effect plots shown in Fig.5 display the effects that a change in weld angle or joint
type have on the hardness of the specimen. Changing from a straight weld to a diagonal weld, results
in an increase in hardness from 101.3 to 102.6 on the Rockwell E scale. This increase is because as the
weld changes from straight to diagonal, it affects a longer distance on the specimen. Although this
change in hardness seems minute, it is significant considering the small range in hardness
measurements. Changing from a flat butt joint to a beveled butt joint showed very minimal effects on
the hardness. The difference in joint type is said to have no significant effect on the hardness.
Figure 6 – Main Effect Plot for the Location of Hardness Measurement on Hardness
The main effect plot shown in Fig.6 shows how the hardness changed with respect to the location
in which the hardness was measured. The weld is positioned at location “0” and measurements were taken
at ¼”, ½” and 1” on both sides of the weld. It can be seen that the hardness increases nearer to the weld.
The hardness on the weld is lower possibly because of a slightly different cooling rate or alloy of steel.
Because of the shape of the plot in Fig.6, it is said that the location of the hardness measurements has a
significant factor on the hardness. More simply said, the hardness changes significantly with respect to the
distance from the weld.
Figure 7 – Normal Plot of Residuals for Hardness
Figure 7 shows the normal probability plot for the hardness measurements. Because the
majority of the points fall very near to the fit line, it is safe to assume that the data is normally
distributed and reliable.