In industrial and agricultural production and daily life, there are many cases of lid cracking caused by thermal expansion and cold 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 fracture strength of the rope. After improving the derivation method and extension concept, new structural functions have been obtained.

1 Characteristics and strain analysis of the cover

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

2 Stress Analysis

2.1 The effect of deformation on stress

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

2.2 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 the fluidity, The disc part of the cover is mainly arranged in a radial direction due to the radial flow. The radial tensile strength of the plastic cover after cooling and molding is high, and the chord tensile strength will be significantly lower than the radial direction. Under the shrinkage rate, it is prone to radial cracking. The crystallographic orientation of the polymer material has a significant effect on the strength, which can be learned from the mechanical properties of the biaxially oriented polypropylene film BOPP. For example, the PVC packing tape with 1:1 filling has a significant difference in warp and weft strength after stretching and shaping. The mechanical strength and even the air permeability of plastics are related to factors such as whether there are fillers, the shape of the fillers, and whether the linear macromolecules are crystallized. 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 center-gate injection-molded polystyrene (PS), transparent discs and lid-like PS trays. The statistical data show that the impact cracks are generally radial; The radial bending performance of PS is much higher than that in the chord direction. Under the action of the chordwise bending moment, the fan-shaped PS specimen or the PS thin disk is easily fractured along the radial flow line.

3 Influence of radial concession of cover ring structure on stress

The actual mechanism of the cover at work is the inner part and the cover, and the mutual influence between the two is external force. For the convenience of 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 Influence of concessions on radial and chord stress performance

When the disc part of the cover shrinks radially, due to the flexibility of the polymer material, a certain degree of creep will occur in the connecting corner of the cover ring and the disc part, that is, the cover ring part is given a certain reform ability (reform ability). ), the result of the concession reduces the stress generated by the radial obstruction. Since the material in the chord direction forms a closed ring, the ring material itself is involved in each other after the chord direction shrinks, and the actual effect is no concession.

3.2 Contribution of cover ring valgus deformation rate to chord stress

After the disc part retreats radially, the annular cover ring is subjected to a moment of eversion. Assume that the contact point between the cover ring and the internal object is O, and the length ratio of the force arms 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 at 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 B of the cover ring is everted around the O point. In order to simplify the calculation, a rigid body model is adopted, and the horizontal distance between the bottom edge B of the everted cover ring and the contact fulcrum O between the inner object and the cover ring is △r=α△R=lB·△R/lA. Since the natural position of the cover ring after shrinking should be at R-△R, the horizontal distance between the lower edge B and the upper edge A after being obstructed and everted:

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 bottom edge B is everted is the upper edge A and the disc edge (1+α)(1+△R /R) times. in. With the change of the position of the fulcrum O, α>1 in many cases, so the chordwise relative deformation of the lower edge of the cover ring B is much larger than the relative chordwise deformation of 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, the lower edge of the cover ring is deformed according to the The length ratio of the arms on both sides of the point is related, which can reduce the position of the fulcrum O; increase the radial allowance of the cap, and make the bottle mouth slightly inwardly inclined to reduce the internal stress moment and reduce the internal stress. Adding a telescopic ring along the radial direction on the edge of the disc portion of the cover can reduce the deformation of the disc edge, and ultimately reduce the displacement of the upper and lower edges of the ring portion, thereby greatly reducing the internal resistance caused by the chordwise deformation of the ring. At present, some cover-shaped products are designed with an annular protruding structure based on the edge structure of the object to be buckled, which can reduce radial resistance, but cannot avoid chord stress. The flexibility of polymer materials decreases at low temperature, which directly affects the low-temperature stability of the lid-shaped 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 chordwise shrinkage are consistent, and the directionality of the free shrinkage stress on the disk surface is not significantly affected. The radial retreat of the cover reduces the generation of radial stress, but there is no room for retreat in the chord direction, which can generate greater stress. The relative deformation rate of the ring caused by the eversion trend of the lower edge of the cover ring is large, which expands the chord stress on the edge of the cover ring, which is the primary cause of shrinkage cracking. The radially oriented crystallization during the injection molding of polymer materials weakens the chordwise strength and is also a cause of cracking of the plastic cover. Taking targeted measures can reduce the cracking tendency.

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