State of mental tension (stress)

Every person feels the manifestation of feelings of tension or a feeling of being wound up; more often this occurs in moments of strong psycho-emotional stress. In healthy people, these sensations disappear within 1-2 hours; some take a little longer. However, for some people these sensations can be fixed and they remain for a long period. In such cases, it is already worth talking about the presence of a breakdown of higher nervous activity and seeking qualified help becomes an obvious necessity.

Brain Clinic specialists have extensive experience in treating various breakdowns of higher nervous activity and will be able to correctly and safely restore the body’s functioning without any side or negative effects on it.

Don't be patient and wait for it to go away on its own! In itself, without the participation of a qualified doctor, it is extremely rare, and why endure such conditions!

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The concept of stress at a point

Based on the assumption of body continuity, we can assume that internal forces are continuously distributed over the entire section.
ΔA at an arbitrary point

, and the resultant of the internal forces on this area will be denoted by
ΔR
. Attitude

represents the average voltage at a given site.

If the area ΔA

decrease, then in the limit we obtain the total voltage at the point

Total voltage p

can be decomposed into three components: along the normal to the section plane and along two axes in the section plane.
The projection of the total stress vector p
onto the normal is denoted by
σ
and is called
normal stress
.

Components in the section plane are called shear stresses

and are denoted by
τ
.
Depending on the location and name of the axes, the designations σ
and
τ
are provided with a system of indices.

Causes of tension in galvanic coatings.

1. What are internal stresses?

Electroplating and chemical coatings are always different from pure metals obtained by metallurgical methods. They have a distorted crystal structure and contain inclusions, which leads to their tension, tending to return the system to a stable relaxed state. To understand the mechanism of action of internal stresses, consider a thin model cathode, which is coated on only one side. During coating deposition, such a cathode can either remain in a straight state or bend under the action of a superposition of two forces (Figure 1):

Figure 1 - Diagram of positive and negative internal voltages in electroplated coatings.

— Tensile force. The bend goes towards the anode, the deposit tends to reduce its volume (Figure 1 a). Indicated by a “+” sign. — Compression force. The bending goes in the opposite direction from the anode, the deposit tends to increase its volume (Figure 1 b). Indicated by the sign “-“. The main reasons for the stress of electroplating are changes in: 1. Crystal lattice parameters. 2. Distance between coating crystals. 3. The size of the sediment crystals (merging of small ones into large ones). 4. Volume of the coating (due to the formation of intermetallic compounds and other chemical compounds of the coating metal with impurities). Let's take a closer look at them. 2. The nature of internal stresses in coatings. 2.1 Changing the parameters of the metal crystal lattice.

As mentioned earlier, electroplated coatings have a distorted, nonequilibrium crystal lattice that tends to stabilize, resulting in the formation of internal stresses in the deposit. There are three possible ways of crystal distortion: 1. The electrical double layer formed in the near-cathode space during electrodeposition has a very high transition resistance, which can be 8-9 orders of magnitude greater than the electrolyte resistance. For this reason, there is a sharp increase in the energy of thermal vibrations of the ions that are discharged and incorporated into the coating, which is externally expressed in the heating of the near-cathode layer (the release of Joule heat). This circumstance greatly affects the parameters of the crystal lattice of the coating. The higher the coating deposition overvoltage, the stronger the temperature effects experienced by the ions of the deposited metal, the more the lattice is distorted and the more strongly the deposit tension increases (Table 1).

Table 1 - Relationship between the magnitude of the deposition overvoltage of some electroplated coatings and the internal stresses in them.

2. Simultaneously with the deposition of the base metal in electroplating, side reactions almost always occur, one of which may be the reduction of impurities (hydrogen, organics, other metals), which can be built into the crystal lattice of the coating. Inclusion leads to distortions of the crystal lattice due to the energy heterogeneity of the structural elements included in it. It has been established that an increase in the parameters of the crystal lattice leads to an increase in internal stresses and vice versa. For example, the inclusion of aluminum and zinc in a copper coating increases the lattice parameters and deposit tension, and reduces it with nickel. 3. As the coating thickness increases, the crystal lattice of the deposit is subject to distortion. This is due to an increase in the size of the crystals and a mismatch in the lattice parameters of the outer and inner layers of the deposit (they depend on the interaction forces of nearby atoms or ions). In this case, two cases are possible: a. In crystals with covalent bond types, the atoms of the inner layers are attracted by a larger number of atoms than the atoms of the outer layers, so the lattice parameters of the inner layer will be smaller than those of the outer layer. b. In ionic-type crystals, the ions of the inner layers are more repelled by neighboring ions than the ions of the outer layer, therefore, for them, the opposite trend in the crystal lattice parameters is observed, compared to covalent crystals (the parameters in depth will be greater than on the outside). In dynamics, the outer layers gradually become internal and forces arise in the coating, tending to change the lattice parameters, which leads to tension. Considering that in a fine-crystalline sediment, most of the volume is represented by the volume of the outer layers of crystals, it will exhibit a greater tendency for the crystal lattice parameters to change as it grows, in comparison with coarse-crystalline coatings. Therefore, at the same thickness, fine-crystalline deposits are more stressed than coarse-crystalline deposits. 2.2 Changing the distance between crystals.

The inclusion of foreign particles in the coating can lead not only to changes in the parameters of the crystal lattice, but also to changes in the distance between the crystals.
In this case, the particles can both enter the lattice structure and be localized at the grain boundaries. There are 2 reasons for the change in the distance between the crystals: 1. If there are surfactants in the electrolyte, their molecules can be adsorbed on the cathode and deformed in the electric double layer under the influence of an electric field. This manifests itself in the extension of the surfactant molecule along a certain vector. Continuing to build up the coating leads to the fact that the boundary of the electric double layer shifts towards the solution, and the effect of the electric field on the sorbed surfactant molecules disappears. At the same time, they relax and strive to return to their original state, pushing the crystals apart and causing internal tension. 2. If impurities are unevenly included in the deposited coating between the metal crystals, then later due to diffusion they will begin to be redistributed throughout the volume of the deposit, which will cause its tension. This mechanism of changing the distance between crystals is very typical during hydrogenation of nickel. The nickel layers closest to the base contain more hydrogen than the overlying ones, and when it is redistributed throughout the volume of the coating, internal stresses arise. 2.3 Changing crystal sizes.
The general tendency of crystals in the coating is to enlarge, which is associated with their desire to reduce their surface energy.
At the same time, the volume decreases. Obviously, internal stresses must arise in this case. Heat treatment accelerates this process, and the adsorption of surfactants at the boundaries of crystal grains slows it down. According to one idea, the process of enlargement can proceed from a metastable system of small nuclei with a high supply of free energy to a stable system of larger crystals. According to another idea, the process begins with the formation of small nuclei with one type of stable crystalline structure, but as the crystals grow, they transform into another, more favorable form for this size (for example, chromium begins to precipitate in a hexagonal lattice, and ends in a cubic lattice). When coatings are hydrogenated, the crystal size can also change under excess hydrogen pressure. In this case, the crystals are deformed or destroyed. This mechanism makes a serious contribution to the internal stresses of the coatings, the deposition of which is accompanied by intense hydrogen evolution. 2.4 Formation of chemical compounds.
If, during electrocrystallization, impurities that are capable of forming chemical compounds with the base metal are included in the coating, then the volume of the deposit can locally change under their influence. In such zones, internal stresses will logically arise.

Relationship between stresses and internal forces

Let us establish a connection between stresses and internal forces arising in the cross section of the rod. For this purpose, we select an infinitesimal area dA

and apply elementary forces
σ dA, τx dA, τy dA
.

Summing up the projections of these elementary forces, as well as their moments relative to the Ox, Oy, Oz axes, we find;

The “A” sign for the integral indicates that integration is carried out over the entire cross-sectional area. The given formulas make it possible to determine the resultants of internal forces through stresses, if the law of distribution of the latter over the cross section is known.

The inverse problem cannot be solved using these equations alone, since the same amount of internal force, for example N

, different laws of distribution of normal stresses over a section may correspond.

One of the main problems of resistance of materials is the problem of determining stresses through the resultant internal forces. It turns out that this problem can only be solved by considering, in parallel with the equilibrium conditions, the conditions of deformation of the beam.

Manifestations of tension and nervousness

When feeling tense and overexcited, a person’s performance suffers, as the activity of higher mental functions is disrupted: memory suffers, the person becomes more forgetful; attention is impaired, a feeling of absent-mindedness appears; perception of the surrounding world narrows; thinking becomes more viscous, rigid, and stiff, and the flexibility of thought processes disappears.

Also, feelings of tension and agitation have a negative impact on the emotional-volitional sphere of a person. Aggression and irritability towards others may begin to appear. Emotions become uncorrectable, and an anxious background and/or depressive feelings may appear.

In a short time, the mood can change from excited to extremely depressed, for no apparent reason. Volitional activity is not enough for long-term activity. All this speaks of asthenia (exhaustion) of the nervous system.

Symptoms that may accompany feelings of tension or nervousness

• Feeling of constant or frequent anxiety.
• Nervousness and internal trembling.
• A feeling of constant or frequent fear.
• Strong, rapid heartbeat or extrasystoles.
• Feeling tense or on edge.

In our rather tense time, associated with political and social instability, people quite often feel a feeling of tension and irritability bordering on irritability.

Linear stress state

A stress state is called linear or uniaxial if two principal stresses are zero.

Strength testing under linear stress state is carried out according to the strength condition:

In a complex stress state, strength testing is carried out according to strength hypotheses based on equivalent stress:

Value σeq

is determined based on the accepted equivalence criterion underlying one of the fracture hypotheses or strength hypotheses, in which a complex stress state is replaced by an equivalent tension or compression.