Methods, program products, and systems for estimating the stress-strain relationship of a toughened structural adhesive polymer
View Patent ↗Methods, program products, and computer systems for estimating a stress of a toughened structural adhesive polymer are provided. One method comprises selecting a strain, a strain rate, a temperature, or a combination thereof at which the stress is to be estimated. A value of a strain-hardening stress of the toughened structural adhesive polymer is determined, wherein the value of the strain-hardening stress is dependent on the temperature and the strain. A value of a non-strain-hardening stress of the toughened structural adhesive polymer is determined, wherein the value of the non-strain-hardening stress is dependent on the strain, the strain rate, and the temperature. The value of the strain-hardening stress is added to the value of the non-strain-hardening stress to obtain an estimated total stress.
1. A method for estimating a total stress of a toughened structural adhesive polymer, the method comprising the steps of:
receiving via an input device a strain, a strain rate, a temperature, or a combination thereof at which the total stress is to be estimated;
accessing from a memory device computer instructions and causing the computer to perform:
determining a value of a strain-hardening stress of the toughened structural adhesive polymer, wherein strain-hardening stress of the toughened structural adhesive polymer is assigned a value of zero if the temperature is no greater than about 23° C. and wherein the strain-hardening stress is determined using an equation:
σ
H
=
11
×
T
(
°
C
.
)
-
23
°
C
.
82
°
C
.
-
23
°
C
.
×
ɛ
,
if the temperature is greater than about 23° C., wherein σ H is in units of megapascals (MPa), wherein ε is the strain, T is the temperature, and wherein constants 11, 23° C., and 82° C. deviate by about zero to about ±5° C.;
determining a value of a non-strain-hardening stress of the toughened structural adhesive polymer, wherein the value of the non-strain-hardening stress is dependent on the strain, the strain rate, and the temperature; and
adding the value of the strain-hardening stress to the value of the non-strain-hardening stress to obtain an estimated total stress.
2. The method of claim 1 , wherein the step of determining a value of the non-strain-hardening stress comprises the steps of:
determining a value for a baseline stress (σ 0 ), a strain-rate-dependent stress (φ), and a temperature-dependent factor (η); and
multiplying the values of the baseline stress, the strain-rate-dependent stress and the temperature-dependent factor together.
3. The method of claim 2 , wherein the step of determining a value for a baseline stress (σ 0 ), a strain-rate-dependent stress (φ), and a temperature-dependent factor (η) comprises determining the value for the baseline stress using an equation:
σ 0 (ε)=59.5×(1 −e −45·ε ),
wherein σ 0 (ε) is in units of megapascals and wherein constants 59.5, 1, and −45 deviate by from about zero to about ±5%.
4. The method of claim 2 , wherein the step of determining a value for a baseline stress (σ 0 ), a strain-rate-dependent stress (φ), and a temperature-dependent factor (η) comprises determining the value for the strain-rate-dependent stress using an equation:
φ
(
ɛ
′
,
T
)
=
1
+
18.2
100
-
1.07
·
T
×
lg
(
ɛ
′
/
ɛ
′
0
)
,
wherein φ({acute over (ε)}, T) is unitless, wherein {acute over (ε)} 0 is a reference strain rate, and wherein constants 1, 18.2, 100, and 1.07 deviate by from about zero to about ±5%.
5. The method of claim 2 , wherein the step of determining a value for a baseline stress (σ 0 ), a strain-rate-dependent stress (φ), and a temperature-dependent factor (η) comprises determining the value for the temperature-dependent factor using an equation:
η
(
T
)
=
1
-
(
T
+
40
129
)
0.75
,
wherein η(T) is unitless and wherein constants 1, 40, 129, and 0.75 can deviate by from about zero to about ±5%.
6. The method of claim 1 , further comprising the step of selecting a second strain, a second strain rate, a second temperature, or a combination thereof and repeating the steps of determining and adding to obtain a second estimated total stress of the toughened structural adhesive polymer.
7. A non-transitory computer readable medium containing a computer program product comprising a computer program for estimating a total stress of a structural adhesive polymer at a selected strain, a selected strain rate, and a selected temperature, the:
computer program configured to at least facilitate:
determining a value of a strain-hardening stress of the toughened structural adhesive polymer, wherein the strain-hardening stress of the toughened structural adhesive polymer is assigned a value of zero if the temperature is no greater than about 23° C. and wherein the strain-hardening stress is determined using an equation:
σ
H
=
11
×
T
(
°
C
.
)
-
23
°
C
.
82
°
C
.
-
23
°
C
.
×
ɛ
,
if the temperature is greater than about 23° C., wherein σ H is in units of megapascals (MPa),
wherein ε is the strain, and wherein constants 11, 23° C., and 82° C. deviate by about zero to about ±5° C.;
determining a value of a non-strain-hardening stress of the toughened structural adhesive polymer, wherein the value of the non-strain-hardening stress is dependent on the selected strain, the selected strain rate, and the selected temperature; and
adding the value of the strain-hardening stress to the value of the non-strain-hardening stress to obtain an estimated total stress.
8. The non-transitory computer readable medium of claim 7 , wherein the computer program is configured to at least facilitate determining a value of the non-strain-hardening stress by:
determining a value for a baseline stress (σ 0 ), a strain-rate-dependent stress (φ), and a temperature-dependent factor (η); and
multiplying the values of the baseline stress, the strain-rate-dependent stress, and the temperature-dependent factor together.
9. The non-transitory computer readable medium of claim 8 , wherein the computer program is configured to at least facilitate determining the value for the baseline stress using an equation:
σ 0 (ε)=59.5×(1 e −45·ε ),
wherein σ 0 (ε) is in units of megapascals and wherein constants 59.5, 1, and −45 deviate by from about zero to about ±5%.
10. The non-transitory computer readable medium of claim 8 , wherein the computer program is configured to at least facilitate determining the value for the strain-rate-dependent stress using an equation:
φ
(
ɛ
′
,
T
)
=
1
+
18.2
100
-
1.07
·
T
×
lg
(
ɛ
′
/
ɛ
′
0
)
,
wherein ε({acute over (ε)}, T) is unitless, wherein {acute over (ε)} 0 is a reference strain rate, and wherein constants 1, 18.2, 100, and 1.07 deviate by from about zero to about ±5%.
11. The non-transitory computer readable medium of claim 8 , wherein the computer program is configured to at least facilitate determining the value for the temperature-dependent factor using an equation:
η
(
T
)
=
1
-
(
T
+
40
129
)
0.75
,
wherein η(T) is unitless and wherein constants 1, 40, 129, and 0.75 deviate by from about zero to about ±5%.
12. A computer system for estimating a total stress of a toughened structural adhesive polymer at a selected strain, a selected strain rate, and a selected temperature, the computer system comprising:
a processor configured to at least facilitate:
receiving input signals derived from the selected strain, the selected strain rate, and the selected temperature;
determining a value of a strain-hardening stress of the toughened structural adhesive polymer, wherein the value of the strain-hardening stress is dependent on the selected temperature and the selected strain;
determining a value of a strain-hardening stress of the toughened structural adhesive polymer, wherein the strain-hardening stress of the toughened structural adhesive polymer is assigned a value of zero if the selected temperature is no greater than about 23° C. and wherein the strain-hardening stress is determined using an equation:
σ
H
=
11
×
T
(
°
C
.
)
-
23
°
C
.
82
°
C
.
-
23
°
C
.
×
ɛ
,
if the selected temperature is greater than about 23° C., wherein σ H is in units of megapascals (MPa), wherein ε is the selected strain, and wherein constants 11, 23° C., and 82° C. deviate by about zero to about ±5° C.;
determining a value of a non-strain-hardening stress of the toughened structural adhesive polymer, wherein the value of the non-strain-hardening stress is dependent on the selected strain, the selected strain rate, and the selected temperature; and
adding the value of the strain-hardening stress to the value of the non-strain-hardening stress to obtain an estimated total stress; and
an output device coupled to the processor and configured to at least facilitate displaying the estimated total stress.
13. The system of claim 12 , wherein the processor is configured to at least facilitate determining a value of the non-strain-hardening stress by:
determining a value for a baseline stress (σ 0 ), a strain-rate-dependent stress (φ), and a temperature-dependent factor (η); and
multiplying the values of the baseline stress, the strain-rate-dependent stress and the temperature-dependent factor together.
14. The system of claim 13 , wherein the processor is configured to at least facilitate determining the value for the baseline stress using an equation:
σ 0 (ε)=59.5×(1 e −45· ),
wherein σ 0 (ε) is in units of megapascals and wherein constants 59.5, 1, and −45 deviate by from about zero to about ±5%.
15. The system of claim 13 , wherein the processor is configured to at least facilitate determining the value for the strain-rate-dependent stress using an equation:
φ
(
ɛ
′
,
T
)
=
1
+
18.2
100
-
1.07
·
T
×
lg
(
ɛ
′
/
ɛ
′
0
)
,
wherein φ({acute over (ε)}, T) is unitless, wherein {acute over (ε)} 0 is a reference strain rate, and wherein constants 1, 18.2, 100, and 1.07 deviate by from about zero to about ±5%.
16. The system of claim 13 , wherein the processor is configured to at least facilitate determining the value for the temperature-dependent factor using an equation:
η
(
T
)
=
1
-
(
T
+
40
129
)
0.75
,
wherein η(T) is unitless and wherein constants 1, 40, 129, and 0.75 can deviate by from about zero to about ±5%.
17. The system of claim 12 , further comprising an input device coupled to the processor and configured to at least facilitate obtaining the selected strain, the selected strain rate, the selected temperature, or a combination thereof and transmit data indicative of the selected strain, the selected strain rate, the selected temperature, or a combination thereof to the processor.
18. The method of claim 1 , further comprising sending to an output device the estimated total stress and causing the output device to display the estimated total stress on a display device.