Grips for a linear fracture testing machine and method of designing same
Test fixture grips for testing quasibrittle materials, such as fiber-polymer composites are provided having increased mass and stiffness relative to standard test grips to provide for obtaining postpeak measurements. The design is based on static analysis (using the second law of thermodynamics), confirmed by dynamic analysis of the test setup as an open system. Dynamic analysis of the test setup as a closed system with PID controlled input further indicates that the controllability of postpeak softening under CMOD control is improved not only by increasing the grip stiffness but also by increasing the grip mass.
1. A system comprising:
a linear fracture testing machine configured to test a specimen, wherein the linear fracture testing machine has a frame stiffness K m and the specimen has an incremental stiffness K s ;
grips configured to secure to the linear fracture testing machine and secure the specimen, wherein the grips are configured to have a stiffness K g to enable stable postpeak measurements of the specimen under a Crack Mouth Opening Displacement (CMOD) control, wherein a combined stiffness of the linear fracture testing machine and the grips K mg =1/(1/K m +1/K g ), and a total stiffness of the specimen, the linear fracture testing machine, and the grips K t =1/(1/K m +1/K g )+K s >−0-;
an extensometer configured to measure the Crack Mouth Opening Displacement (CMOD) of the specimen; and
a closed-loop servo control system coupled to the linear fracture testing machine, the grips, and the extensometer, to control testing of the specimen based on a Proportional-Integrative-Differential (PID) signal.
2. The system of claim 1 , wherein the grips are configured to enhance controllability of the stable postpeak measurements based on a mass and the stiffness K g of the grips.
3. The system of claim 1 , wherein the specimen is a quasi-brittle material and has a negative incremental stiffness.
4. The system of claim 1 , wherein K m is about 200 MN/m , K s is about −0.830 MN/m, and K g is about 192.4 MN/m, and the mass of the grips is about 9.419 kg.
5. The system of claim 1 , wherein the grips have a stiffness K g =1/(K s /K t −1/K m +1K t ) >−0-.
6. The system of claim 5 , wherein K m is about 200 MN/m, K s is about − 0 . 830 MN/m, and K g is about 192.4 MN/m, and the mass of the grips is about 9.419 kg.
7. Grips, configured to:
secure to a linear fracture testing machine;
secure a specimen that is a quasi-brittle material and has a negative incremental stiffness;
and
have a stiffness K g to enable stable postpeak measurements of the specimen under a Crack Mouth Opening Displacement (CMOD) control, wherein a combined stiffness of the linear fracture testing machine and the grips K mg =1/(1/K m +1/K g ), and a total stiffness of the specimen, the linear fracture testing machine, and the grips K t =1/(1/K m +1/K g ) +K s >−0-, wherein each of the grips comprises a base and first and second parallel legs extending from the base defining a slot for receiving the specimen, and each of the grips is massive in the base to enhance controllability of the stable postpeak measurements based on a mass of the grips.
8. The grips of claim 7 , wherein each of the first and second parallel legs has an aperture therein for receiving a pin by which the specimen is secured to the grip.
9. The grips of claim 7 , wherein K m is about 200 MN/m , K s is about −0.830MN/m, and K g is about 192.4 MN/m, and the mass of the grips is about 9.419 kg.
10. The grips of claim 7 , wherein the grips have a stiffness K g =1/(K s /K t −1/K m +1/K t )>−0-.
11. The grips of claim 10 , wherein Km is about 200 MN/m , K s is about −0.830 MN/m, and K g is about 192.4 MN/m, and the mass of the grips is about 9.419 kg.
12. A method of manufacturing grips for a linear fracture testing machine, wherein the grips are manufactured to have a mass and a stiffness to enable stable postpeak measurements of a specimen under a Crack Mouth Opening Displacement (CMOD) control, the specimen has a negative incremental stiffness, and the method comprises:
inputting variables comprising:
an incremental stiffness (K s <0) of the specimen;
a stiffness of the linear fracture testing machine (K m >0);
a mass of the specimen;
a mass of the linear fracture testing machine;
a time delay of the linear fracture testing machine; and
Proportional-Integrative-Differential (PID) parameters for the combination of the linear fracture testing machine, the grips, and the specimen;
determining the mass and the stiffness of the grips by solving
[
-
λ
1
0
0
0
-
1
m
(
K
g
+
∂
K
s
∂
x
1
)
-
λ
K
g
m
0
0
0
0
-
λ
1
0
R
1
-
β
K
M
M
R
2
-
K
M
τ
M
-
Km
γ
M
-
λ
1
0
0
0
-
λ
]
(
28
)
R
1
=
K
g
-
α
K
M
M
+
K
M
τ
M
[
γ
+
β
∂
K
s
/
∂
x
1
+
K
g
m
]
(
29
)
R
2
=
-
K
M
+
K
g
M
+
βτ
K
g
K
M
mM
(
30
)
so that the eigenvalues are negative; and
manufacturing the grips having the determined mass and stiffness, wherein each of the grips comprises:
a base having one of a threaded shaft or a threaded bore for securing the grip to the linear fracture testing machine; and
first and second parallel legs extending from the base of each grip.
13. The method of claim 12 , wherein the determined stiffness of the grips K g =1/(K s /K t −1/K m +1/K t ) >−0-, wherein
K s , is an incremental stiffness of the specimen;
K t is a total stiffness of the specimen, the linear fracture testing machine, and the grips; and
K m is the stiffness of the linear fracture testing machine.
14. The method of claim 12 , wherein each of the manufactured grips is massive in the base.
15. The method of claim 12 , wherein each leg of the grips comprises an aperture therein for receiving a pin by which the specimen is secured to the grips.