In industrial and agricultural production and daily life, there are many cases of cover cracking due to thermal expansion and contraction, which directly affects the circulation and use of commodities, causes liquid leakage, and even leads to fire accidents. In elastic mechanics, the deformation is proportional to the stress. Hangzhou Dianzi University uses the method of deformation analysis to solve the problem of the internal stress distribution calculation and the breaking strength of the rope. After improving the derivation method and the extension concept, it has obtained new structural functions.

1 Cap characteristics and strain analysis

The geometric shape of the cover can be regarded as a combination of a disc and a ring. For a disk with a radius of and. If the radial and chord shrinkage rates of the disc part are the same, the relative radial shrinkage rate PD=△R/(2R)=△R/R, the relative perimeter shrinkage rate PC=2π△R/(2πR)=△ R/R, compared with PC=PD=△R/R, that is, there is no obvious advantage in the relative contraction rate in the radial and chord direction.

2 Stress analysis

2.1 The influence of deformation on stress

According to the stress is proportional to the relative elongation, the shrinkage stress in the warp, weft, and direction of the isotropic material is equivalent, and the tear direction of the cover should be irregular. According to the tensile strength of the polymer material and the actual radial force converges in the center of the circle, even if the stress exceeds the strength of the material, the fracture should occur near the center of the stress concentration. The above 2 points are in line with the fact that the crack occurs at the edge of the cover ring.

2.2 The influence of polymer material molding process on mechanical properties

Considering that LDPE has many branches, the crystallinity is about 55%~60%; HDPE is linear, with few branches, and the crystallinity is 85%~90%. When injection molding from the center of the disc, due to fluidity, Due to the radial flow, the radial flow of the disc part of the cover causes the linear alignment of the polymer material to be mainly radial. After cooling and forming, the radial tensile strength of the plastic cover is high, and the chord tensile strength will be significantly lower than that of the radial direction. Under the shrinkage rate, it is easy to crack in the radial direction. The crystal orientation of polymer materials has a significant effect on strength, which can be understood from the mechanical properties of the biaxially oriented polypropylene film BOPP. For example: the PVC packing belt with filling according to 1:1 has a significant difference in warp and weft strength after being stretched and shaped. The mechanical strength and even air permeability of plastics are related to the presence of fillers, filler morphology, and whether linear macromolecules are crystallized or not. After the molded polymer is stretched and oriented, its tensile strength is greatly improved, and it is easy to tear in the weft direction. Cracks (typically such as strapping). The author has done a large number of impact tests on polystyrene (PS), transparent discs and similar cap-shaped PS trays molded by the center gate. Statistics show that the impact cracks generally proceed in the radial direction; local sample bending tests show that, The radial bending performance of PS is much higher than the chord direction. Under the action of the bending moment in the chord direction, the fan-shaped PS specimen or the PS thin disc is easily broken along the radial flow line.

3 The influence of radial concession of cover ring structure on stress

The actual mechanism of the cover when it is working is the inner object and the cover, and the mutual influence between the two is an external force. In order to facilitate analysis, it is assumed that the content does not shrink with temperature changes, and the diameter is the same as that of the cover.

3.1 The influence of concession on the performance of radial and chordal stress
When the disc part of the cover shrinks radially, due to the flexibility of the polymer material, the connecting corners of the cover ring and the disc part will have a certain degree of creep, which gives the cover ring part a certain degree of concession (reform ability). ), the result of concession reduces the stress generated by the radial resistance. Since the chord-direction material forms a closed ring, the ring-shaped materials themselves are involved in each other after the chord-direction shrinks. The actual effect is no concession. As a result, the chord-direction stress is greatly manifested and the tendency of cracking is formed.

3.2 Contribution of the eversion deformation rate of the cover ring to the chordal stress

After the disc part radially retreats, the annular cover ring receives the moment of eversion. Suppose the contact point between the cover ring and the inner object is O, and the ratio of the arm length at both ends of O is α=lB/lA, as shown in Figure 2. After shrinking, the natural position of the cover ring should be R-△R outside the center of the circle. At this time, the circumferential length of the cover ring is C1=2π(R-△R). Due to the obstruction of the contents of the cover, under the action of the radial contraction force of the disc part, the lower edge of the cover ring turns outward around the point O. In order to simplify the calculation, the rigid body model is adopted, and the horizontal distance between the lower edge B of the eversion cover ring and the contact fulcrum O of the inner object and the cover ring is △r=α△R=lB·△R/lA. Since the natural position of the cover ring after contraction should be at R-△R, the horizontal distance between the lower edge B and the upper edge A after being prevented from eversion:

The perimeter expansion rate PC1 of the lower edge B relative to the upper edge A is:

And the relative shrinkage rate of the disc edge PC=△C/C=△R/R, obviously the relative perimeter elongation after the lower edge B eversion is the upper edge A and the disc edge (1+α)(1+△R /R) times. among them. With the change of the position of the fulcrum O, in many cases, α>1, so the relative chordal deformation of the lower edge of the cover ring B is much larger than the relative chordal deformation at the edge of the disc, and the shrinkage crack of the cover coincides with this. Its inevitability.

4 Solutions and measures

In order to reduce the cracking tendency of the cover, it is deformed according to the lower edge of the cover ring. The ratio of the length of the arms on both sides of the point is related, which can reduce the position of the fulcrum O; increase the radial retreat of the cover, and make the mouth of the bottle a slightly inwardly inclined form to reduce the internal stress moment and reduce the internal stress. Adding a telescopic ring in the radial direction to the edge of the disc of the cover can reduce the deformation of the edge of the disc, and finally cause the displacement of the upper and lower edges of the ring to be reduced, thereby greatly reducing the internal resistance caused by the chordal deformation of the ring. At present, some cap-shaped products have designed a ring-shaped protruding structure based on the edge structure of the object to be buckled, which can reduce the generation of radial resistance, but cannot avoid the chordal stress. The flexibility of polymer materials decreases at low temperatures, which directly affects the low temperature stability of the cover structure and enhances the brittleness.

5 Conclusion

The cold shrinkage crack of the cover meets the mechanical analysis conditions from the lower edge of the cover ring. Under the assumption that the warp and weft shrinkage rates are the same, the radial and chord shrinkage are consistent, and there is no significant effect on the directionality of the free shrinkage stress of the disk surface. The radial retreat of the cover reduces the generation of radial stress, but the chords are mutually implicated and have no retreat, which can generate greater stress. The relative deformation rate of the ring caused by the eversion tendency of the lower edge of the cover ring is large, which enlarges the chordal stress at the edge of the cover ring, which is the primary cause of cold shrinkage cracking. The radially oriented crystallization of the polymer material injection molding process weakens the string strength, which is also a reason for the cracking of the plastic cover. The use of targeted measures can reduce the tendency of cracking.