V.V. Goncharenko, P.I. Loboda, M.V. Goncharenko, G.V. Gerasimov

A.O. Tkachenko, M.Heilmaier

Straightened springs as reinforcing members of the shape memory polymer matrix composites

Extremely straightened spiral springs are operable as reinforcing members of

the shape memory polymer matrix composites. Such springs have been given adequate consideration from the industrial standpoint. Degrees of contraction of such springs in the stress-free state have been linked to their index. It is found that extreme deformation of the straightened spring is in keeping with the spring material elasticity limit. This is reflected in the fact that determination of the spring material elasticity limit can result from the spiral spring straightening method to a high degree of accuracy.

Keywords: straightened spring reinforced polymer matrix composites.

1.Intoduction

Production process of the shape memory metal reinforced polymer matrix

composites [1] may be greatly simplifies by the extreme straightening of the reinforcing spiral springs [2]. This shape memory composites on being heated during constrained conditions generate the great inherent stress cumulative by the extremely straightened reinforcing springs. Before such composites were heated the inherent stresses in the reinforcing springs are absorbed by the compressed hardened polymer matrix. On further heating, the softened polymer matrix loses to resist the straightened reinforcing spring shortening. As this takes place, the statically delicate balance is disrupted and a thermal shrinkage of the shape memory composite takes effect. The great reconstruction stress will been generated in such composite material in the event that thermal shrinkage has been going during constrained conditions [3].

Little else has been reported regarding investigation of the extremely straightened reinforcing springs in the shape memory polymer matrix composites.

2. The present state of the art of the extremely straightened springs

The non-linear elasticity of the extremely straightened springs was discussed

previously in articles [1-3]. Attention in this articles focuses on the nonstandard spring extreme straightening. An index J of this nonstandard springs is megascopic. This index J is defined as ratio D₀/d, where D₀ is diameter of a central line of the springs with close coils generated by a paddy wire with diameter d. The magnitude of the indexes J for standard springs fall within the broad range between 8 and 12 units. The deformation of this springs cannot top maximum of 30 percents. In such situations this standard springs have been functioning in the linear area of an elasticity in so far as magnitudes of a maximum shear (near 1%) of its paddy wires should not be exceeded.

The nonstandard springs with indexes over then 100 units can be straightened

and conversely recovered in so far as magnitudes of the maximum shear of the spring paddy wires do not go out from the scope of the linear elasticity limit [4]. As it shown in article [1], the maximal angle φ_m of the spring wire twisting can be computed by the following formula:

φ_m=4Δα_m, (1)

where Δα_m is maximal value of a decrement of a winding angle of the spring:

Δα_m=α_m–α₀. (2)

Parameter α₀ in Eq.2 is the initial winding angle of the stress-free spring.

Maximal winding angle α_m of the extremely straightened spring is equal to π/2.

In such situation, Eq.2 has been demonstrated in the following manner:

Δα_m=0,5π-α₀. (3)

3. Theory

In such a manner formulating, the structures of these angles make it possible to

determine the most important geometrical parameters of the straightened springs. The maximal tangential displacement U_m at the spring wire surface for the length πD₀ per one spring step may be computed by the following formula:

U_m=0,5dφ_m. (4)

A substitution Eq.1 and Eq.2 into Eq.4 gives the following formula:

U_m=d(π-2α₀). (5)

The determination of the maximal relative shear γ_m on the spring wire surface as U_m/(πD) gives the following equation

γ_m=(π-2α₀)/(πJ)^-1. (6)

A maximal degree of the straightened spring reversible elongation can be

computed by the following expression:

λ_m=(sinα₀)^-1. (7)

The initial winding angle α₀ of such spring can be determined by a conversion of Eq.6:

α₀=0,5π(1-γ_mJ). (8)

A substitution Eq.8 into Eq.7 gives the following expression:

λ_m={sin[0,5π(1-γ_mJ)]}^-1. (9)

Eq.9 makes possible a computation of the maximal degree λ_m of the reversible

elongation of the nonstandard straightened spiral springs. In stress-free conditions the spring length tends to decrease by a factor to the degree λ_m. From the results obtained it may be concluded that maximal degree λ_m of the straightened spring shortening is equal to the maximal degree of a thermal stress free shrinkage of the appropriate shape memory polymer matrix composites. An increase of the spring index J to 100 -150 units always leads to augmentations of the reconstruction deformation of the stress-free straightened springs.

In such situation on increase of the maximal degree λ_m of the stress-free

shortening of the straightened springs is due to be concerned with a rise in shrinkage degree of the appropriate shape memory polymer matrix composites. Another way of considering the maximal relative shear γ_m on the spring wire surface is by analogy with the spring material elasticity limit, that is to say the material constant. This material constant γ_m for any spring material can be computed by Eq.6. The initial winding angle α₀ in Eq.6 can be determined by the following expression:

α₀=arcsin . (10)

A partial unwinding of the spiral springs has been seen in the process of the

spring straightening. This is reflected in the fact that quantity of the spring coils had declined in number from z₀ to z units. In this situation the initial spring index will be increased from J₀ to J according to expression:

J=J₀z₀/z. (11)

A contraction degree λ_m of the straightened springs in a stress-free state can be

determined as

λ_m=L_ïð/L₀. (12)

where L_ïð is a length of the spring wire; L₀ is a length of the straightened spring in a stress-free state.

4. Experiment

As a check on an agreement between theory and experiment, spiral springs with

closed coils were tailor-made for an extreme elongation from the wire with diameter of 0,45 mm through special techniques. Parameters of such springs are tabulated in Table 1. A results of the experimental data treatment are tabulated in Table 2.

5. Discussion

It turns out that the maximal relative shear on the wire surface of the extremely

straightened spiral springs is always uniquely determined by Eq.6. This has an important bearing on the method of the material constant determination. It is reasonable safe to suggest that the shortening degree of the straightened springs in a stress-free state may be considered as the shrinkage degree of the appropriate shape memory composite in the stress-free state.

6. Conclusion

The procedure of the extremely straightening of the spiral springs is particularly

advantageous for more nearly approximate the actual material constant of the spring wire. It is well established that the maximal relative shear on a surface of the steel spring wire is nearly constant in value. It has been suggested that the method of the spring straightening be used for definition of the stress-free shrinkage degree of the appropriate shape memory polymer matrix composites.

Table 1. Parameters of the extremely straightened spring (experiment)

Parameters	Symbols	Dimension	Number of spring
			I	I I	I I I
Diameter of the spring wire	d	ìì	0,45	0,45	0,45
length of the spring wire	Lïð	ìì	2140	2492	2290
Length of spring in stress-free state	L0	ìì	1100	1661	1915
Initial diameter of the spring with closed coils	D0	ìì	23	19	11
Initial quantity of coils	z0	-	29	42	56
Quantity of coils of the straightened springs	z	-	19	28	31

Table 2. Results of experimental data treatment

Parameters	Number of equation	Symbols	Dimension	Number of spring
				I	I I	I I I
Initial spring index	-	I0	-	51	42,2	29
Spring index	(11)	I	-	79,7	63	44,2
Maximal degree of recoverable deformation	(12)	λm	-	1,94	1,5	1,2
Initial winding angle	(10)	α0	-	0,54	0,73	0,966
Maximal shear on the spring wire surface	(6)	γm	%	0,91	0,83	0,87

Nomenclature

D₀ - diameter of springs, mm; d - diameter of the spring wire, mm; J - spring index; L₀, L_ïð - length of the spring wire, mm; L₀ – length of the spring in a stress-free state, mm; U_m – maximal tangential displacement, mm ; z – number of the spring coils; α₀, α_m- initial and maximal values of the winding angle; Δα – decrement of the winding angle; γ_m – maximal value of shear; λ_m – maximum degree of elongation of spring; π-number; φ_m-maximum twist angle.

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