JP7463220B2 - Method for calculating elastic modulus of fiber sample, system for calculating elastic modulus of fiber sample, method for evaluating hair cosmetic product, method for producing hair cosmetic product, and method for determining hair cosmetic product - Google Patents

Description

Article 30, paragraph 2 of the Patent Act applies 1. Publication date June 3, 2020 2. Publication Proceedings of the 2020 Annual Meeting of the Society of Fiber Science and Technology 3. Distributor Masato Isobe

The present invention relates to a method for calculating the elastic modulus of a fiber sample, a system for calculating the elastic modulus of a fiber sample used in the method for calculating the elastic modulus of a fiber sample, a method for evaluating hair cosmetics for treating hair using the calculation of the elastic modulus of a fiber sample, a method for producing hair cosmetics based on the evaluation results, and a method for determining hair cosmetics.

The feel of an object made of a fiber material varies depending on the bending stiffness and elastic modulus of the fiber material. A method for measuring the bending stiffness and elastic modulus of each fiber sample contained in a fiber material is known, for example, as described in Non-Patent Document 1.

Methods for measuring the elastic modulus of a fiber sample, which is a part of a fiber material, are known, for example, from the methods described in Patent Documents 1 and 2 and Non-Patent Document 2. These documents show a method for calculating the elastic modulus of hair, which is a typical fiber sample.

JP 2012-225652 A JP 2005-331283 A

Journal of the Society of Cosmetic Chemists, Vol 29, No.8 p469-485 J. Soc. Cosmet. Chem. Jpn Vol.36, No3 p207-p216

However, in the method described in Patent Document 1, many measurements are required to calculate the elastic modulus of the fiber sample. In the method described in Patent Document 2, the elastic modulus is calculated from observation of the cross section of the fiber sample using an atomic force microscope. Observation of a cross section using an atomic force microscope is not easy. Furthermore, in the method described in Non-Patent Document 2, the outer layer of the hair is peeled off in order to measure the elastic modulus of each hair layer. The task of peeling off the outer layer of the hair is not easy and requires a lot of work. In other words, in these methods, it is time-consuming and requires precise observation and work to calculate the elastic modulus of the fiber sample, and it is not easy to determine the elastic modulus of the fiber sample.

The present invention was made with these points in mind, and aims to easily calculate the elastic modulus of a fiber sample.

The first method for calculating the elastic modulus of a fiber sample of the present invention comprises the steps of:
determining a moment of area of inertia of a fiber sample;
a step of fixing only one end of the fiber sample and applying a predetermined load to the other end, and measuring a length between a fixing position of the fiber sample and the other end and an amount of deflection of the other end;
and calculating the elastic modulus of the fiber sample from the second moment of area of the fiber sample, the length between the fixed position of the fiber sample and the other end, and the deflection amount of the other end.

In the first method of calculating the elastic modulus of a fiber sample of the present invention, the step of determining the second moment of area may include a step of measuring the outer diameter of the fiber sample.

A second method for calculating an elastic modulus of a fiber sample according to the present invention is a method for calculating an elastic modulus of each layer of a fiber sample having a plurality of layers made of different materials, the method comprising the steps of:
preparing a number of fiber samples taken from the same subject, the number of fiber samples being equal to or greater than the number of layers in the fiber sample;
Identifying the second moment of area of each layer of each fiber sample;
a step of measuring, for each fiber sample, a length between a fixing position of the fiber sample and the other end and a deflection amount of the other end while fixing only one end of the fiber sample and applying a predetermined load to the other end;
and calculating the elastic modulus of each layer of the fiber sample from the second moment of area of each fiber sample, the length between the fixed position and the other end of the fiber sample, and the deflection amount of the other end.

In the second method of calculating the elastic modulus of a fiber sample of the present invention, the step of determining the second moment of area of each layer may include a step of measuring the outer diameter of the fiber sample and the thickness of each layer.

In the second method of calculating the elastic modulus of a fiber sample of the present invention, the number of fiber samples prepared in the step of preparing the fiber samples may be greater than the number of layers that the fiber samples have.

In the first or second method of calculating the elastic modulus of a fiber sample of the present invention, the fiber sample may be body hair of a mammal.

The system for calculating the elastic modulus of a fiber sample of the present invention comprises:
A device for measuring the second moment of area of a fiber sample;
a device for measuring the length between a fixing position of the fiber sample and the other end and the amount of deflection of the other end while fixing only one end of the fiber sample and applying a predetermined load to the other end;
and a device for calculating the elastic modulus of the fiber sample from the second moment of area of the fiber sample, the length between the fixed position of the fiber sample and the other end, and the amount of deflection of the other end.

In the system for calculating the elastic modulus of a fiber sample of the present invention, the device for measuring the second moment of area of the fiber sample may measure the outer diameter of the fiber sample.

In the system for calculating the elastic modulus of a fiber sample of the present invention, the device for calculating the elastic modulus of the fiber sample may calculate the elastic modulus of the fiber sample from the second moment of area for each of a plurality of fiber samples, the length between the fixed position and the other end of the fiber sample, and the amount of deflection of the other end.

The method for evaluating a hair cosmetic composition of the present invention comprises the steps of:
Calculating the elastic modulus of the hair by any of the methods for calculating the elastic modulus of a fiber sample described above;
treating the hair with a hair cosmetic;
calculating the elastic modulus of the hair after treatment with the hair cosmetic composition by any of the methods for calculating the elastic modulus of a fiber sample described above;
and comparing the elastic modulus of the hair before treatment with the hair cosmetic product with the elastic modulus of the hair after treatment with the hair cosmetic product.

The method for producing a hair cosmetic of the present invention includes a step of adjusting the components of the hair cosmetic based on the above-mentioned method for evaluating the hair cosmetic.

The method for determining a hair cosmetic composition of the present invention comprises the steps of:
Receiving a donation of hair;
Calculating the elastic modulus of the provided hair by any of the methods for calculating the elastic modulus of a fiber sample described above;
treating the hair with a hair cosmetic;
calculating the elastic modulus of the hair after treatment with the hair cosmetic composition by any of the methods for calculating the elastic modulus of a fiber sample described above;
and evaluating the suitability of the hair cosmetic for the provided hair by comparing the elastic modulus of the hair before treatment with the hair cosmetic and the elastic modulus of the hair after treatment with the hair cosmetic.

According to the present invention, the elastic modulus of a fiber sample can be easily calculated.

FIG. 1 is a schematic diagram showing the configuration of a system for calculating the elastic modulus of a fiber sample. FIG. 2 is a diagram showing an example of the structure of a fiber sample. FIG. 3 is a side view that shows a schematic diagram of a second moment of area specifying device included in the system for calculating the elastic modulus of a fiber sample. FIG. 4 is a cross-sectional view of an example of a fiber sample. FIG. 5 is a perspective view that shows a schematic diagram of a length measuring device included in the system for calculating the elastic modulus of a fiber sample. FIG. 6 is a side view showing a state before a load is applied to a fiber sample in the length measuring device. FIG. 7 is a side view showing a state in which a load is applied to a fiber sample in the length measuring device.

Figure 1 is a schematic diagram of a calculation system for the elastic modulus of a fiber sample in this embodiment (hereinafter, simply referred to as the "calculation system"). The calculation system 1 can calculate the elastic modulus of a desired fiber sample. As shown in Figure 1, the calculation system 1 has a second moment of area specifying device 10, a length measuring device 20, and an elastic modulus calculation device 30 that receives the value of the second moment of area specified by the second moment of area specifying device 10 and the value of the length measured by the length measuring device 20 and calculates the elastic modulus of the fiber sample.

The fiber sample for which the elastic modulus is calculated may be, for example, mammalian body hair, and may have multiple layers of different materials. In the embodiment shown below, the fiber sample is human hair 50. However, without being limited to this embodiment, the fiber sample may be human body hair other than hair, or may be body hair of other mammals. Alternatively, the fiber sample may be any fibrous object other than mammalian body hair, for example a fiber sample taken from a non-living subject.

2 shows a typical structure of hair. As shown in FIG. 2, hair 50 has cuticle 51 that constitutes the surface of hair 50, cortex 53 that is a main component of the inside of hair 50, and medulla 55 that extends through the center of hair 50. However, the boundary between medulla 55 and cortex 53 is often unclear, and even in some cases, medulla 55 does not exist in hair 50. Therefore, in considering the elastic modulus of hair 50, for simplicity, hereinafter, it is considered that medulla 55 is integrated with cortex 53. In other words, hair 50 is considered to have two layers, that is, cuticle 51 and cortex 53. Note that this embodiment can be similarly applied even when a fiber sample such as hair 50 has three or more layers. In other words, even if hair 50 is considered to have cuticle 51, cortex 53, and medulla 55, it is possible to calculate the elastic modulus in the same way using the system for calculating elastic modulus of fiber sample and the method shown below.

The area second moment specifying device 10 specifies the area second moment of the hair 50. The area second moment specifying device 10 measures the outer diameter and the thickness of each layer of the hair 50 by observing the cross section of the hair 50. The cross section of the hair 50 is, for example, a cut surface exposed by cutting a part of the hair 50, and is observed by a microscope. For this reason, as shown in FIG. 3, the area second moment specifying device 10 has a cutting device 11 for cutting the hair 50 and an imaging device 13 for observing the cross section of the hair 50. The observed cross section of the hair 50 is shown in FIG. 4 as a schematic diagram. The cross section of the hair 50 has a substantially elliptical shape. As the outer diameter of the hair 50, the longest major axis a and the shortest minor axis b in the cross section of the hair 50 are measured. In addition, as the thickness of the layer of the hair 50, the thickness D ₁ of the cuticle 51 in the direction of the major axis of the hair 50 is measured. It is considered that the ratio of the thickness _D1 of the cuticle 51 to the major diameter a of the hair is approximately constant over the entire cross section of the hair 50.

By considering the cross section of the hair 50 as an ellipse, the second moment of area of each layer can be calculated. The outer diameter of the hair 50 and the thickness of each layer can be easily measured, so the second moment of area can be easily obtained. The second moment of area specified by the second moment of area specifying device 10 is the second moment of area in the direction in which the hair 50 is most easily deformed when a load is applied, that is, the direction in which the second moment of area is smallest. For example, if the cross section is an ellipse, the second moment of area specified is the second moment of area in the minor axis direction. A method for specifying the second moment of area from the outer diameter of the hair 50 and the thickness of each layer will be explained in detail in the method for calculating the elastic modulus of the hair 50 described later. Note that the second moment of area specifying device 10 may directly calculate the second moment of area by analyzing an image of the cross section of the hair 50, for example, without considering the cross section as an ellipse. In this case, the second moment of area specifying device 10 may further have an image analysis device capable of calculating the second moment of area by analyzing the image.

The length measuring device 20 measures the length between the fixed position and the other end of the hair 50 and the deflection of the other end while fixing only one end 50a of the hair 50 and applying a predetermined load to the other end 50b. The length measuring device 20 has, for example, a fixing base 21 for fixing a part of the hair 50, an imaging device 23 for imaging from a direction perpendicular to the longitudinal direction of the hair 50, and a load device 25 for applying a predetermined load to the other end of the hair 50, as shown in FIG. 5. In the length measuring device 20, as shown in FIG. 5, the hair 50 is fixed at one end 50a, but the other end 50b is a free end. At this time, it is preferable that the hair 50 is kept approximately horizontal. An image captured in this state is shown in FIG. 6. A predetermined load is applied to the other end 50b of the hair 50 in the state shown in FIG. 6. When a load is applied to the hair 50, as shown in FIG. 7, a portion between the fixed position 50f closest to the other end 50b among the fixed positions of the hair 50 and the other end 50b is deflected. The load is large enough that the deflection of the other end 50b is observed, and small enough that the deflection of the other end 50b does not exceed the elastic limit. For example, the load is 1 mg or more and 2 mg or less. The length measuring device 20 measures the length L between the fixed position 50f and the other end 50b of the hair 50 from an image captured with the other end 50b being loaded. The length measuring device 20 also measures the length (deflection amount) δ of the other end 50b of the hair 50 by comparing an image captured before the load is applied to the other end 50b of the hair 50 and an image captured after the load is applied. The length L between the fixed position 50f and the other end 50b of the hair 50 is long enough to make it easy to observe the amount of deflection when a load is applied, and is short enough not to deform under its own weight. Specifically, the length L between the fixed position 50f and the other end 50b of the hair 50 is, for example, 0.5 mm or more and 2.0 mm or less.

The elastic modulus calculation device 30 receives the values of the second moment of area I of the hair 50, the length L between the fixed position 50f and the other end 50b of the hair 50, and the deflection amount δ of the other end 50b, and calculates the elastic modulus of the hair 50 from these values. In addition to the elastic modulus of the entire hair 50, it can also calculate the elastic modulus E _cu of the cuticle 51 and the elastic modulus E _co of the cortex 53 from the second moment of area I _cu of the cuticle 51 and the second moment of area I _co of the cortex 53. A specific method for calculating the elastic modulus of the hair 50 and the elastic modulus of each layer of the hair 50 will be described in detail later.

Next, a method for calculating the elastic modulus of a fiber sample will be described. As an example of a fiber sample, a method for calculating the elastic modulus of mammalian body hair having multiple layers made of different materials, in particular hair 50 having two layers, a cuticle 51 and a cortex 53, will be described. Note that the method for calculating the elastic modulus of a fiber sample described below can be similarly applied to any fibrous object other than mammalian body hair, for example, a fiber sample taken from a subject other than a living organism.

First, multiple hairs 50 are prepared. These hairs 50 are taken from the same subject. That is, all the multiple hairs 50 prepared are hairs from the same person. The number of hairs 50 prepared is equal to or greater than the number of layers the hair 50 has (2 for the hair 50 of this embodiment). The number of hairs 50 prepared is preferably greater than the number of layers the hair 50 has. That is, in this embodiment, three or more hairs 50 taken from the same person are prepared.

Next, the second moment of area of each hair 50 is specified. The second moment of area can be specified by using, for example, the second moment of area specifying device 10. That is, a part of the hair 50 is cut to expose the cut surface, and the cut surface is observed under a microscope. By observing the cross section, the outer diameter of the hair 50 and the thickness of each layer of the hair 50 are measured. The longest major axis a and the shortest minor axis b are measured as the outer diameter of the hair 50, and the thickness _D1 of the cuticle 51 in the direction of the major axis of the hair 50 is measured as the thickness of each layer of the hair 50. From these measured values, the second moment of area of the entire hair 50 and the second moment of area of the cuticle 51 and the cortex 53 of the hair 50 are specified as follows.

The second moment of area I in the minor axis direction of a fiber sample having an elliptical cross section is given by the following equation, where the major axis of the ellipse is a and the minor axis is b:
The cross section of the hair 50 can be considered as an ellipse with a major axis a and a minor axis b. In this case, I is the second moment of area of the hair 50 in the minor axis direction.

In general, let N be a natural number of 2 or more and n be a natural number less than N, and consider the second moment of area I _n of the nth layer from the outside in a fiber sample having N layers. The ratio R _n of the major axis of the nth layer from the outside to the major axis a of the fiber sample is given by
where D ₀ =0. The ratio R _n of the major axis of the nth layer from the outside to the major axis a of the fiber sample is considered to be approximately constant throughout the fiber sample, so using this R _n , the major axis of the nth layer can be expressed as aR _n and the minor axis as bR _n . Using these, the second moment of area I _n of the nth layer from the outside can be expressed as
Here, R _N+1 =0. From this, the second moment of area I _cu of the cuticle 51 of the hair 50 can be expressed as follows:
The second moment of area _Ico of the cortex 53 of the hair 50 is expressed as follows:
However, since N=2, R ₁ =1, R ₂ =1−2D ₁ /a, and R ₃ =0.

From the above calculations, the area moment of inertia I of the hair 50, the area moment of inertia _Icu of the cuticle 51 _, and the area moment of inertia Ico of the cortex 53 are determined by the area moment of inertia specifying device 10.

Then, for each of these hairs 50, only one end 50a of the hair 50 is fixed and a predetermined load P is applied to the other end 50b, and the length L between the fixed position 50f and the other end 50b of the hair 50 and the deflection amount δ of the other end 50b are measured. To make it easier to observe the deflection of the hair 50, the load P is applied in the direction in which the second moment of area of the hair 50 is small, i.e., in the short diameter direction of the hair 50. The length L between the fixed position 50f and the other end 50b of the hair 50 and the deflection amount δ of the other end 50b can be measured, for example, using a length measuring device 20. That is, by comparing images taken before and after the load is applied to the other end 50b of the hair 50, the length (deflection amount) δ of the movement of the other end 50b of the hair 50 is measured.

Next, the elastic modulus of the entire hair 50 and the elastic modulus of each layer are calculated from the specified second moment of area of each hair 50, the length L from the fixed position 50f to the other end 50b, and the deflection amount δ of the other end 50b. The elastic modulus can be calculated, for example, by inputting the specified second moment of area of each hair 50, the length L from the fixed position 50f to the other end 50b, and the deflection amount δ of the other end 50b into the elastic modulus calculation device 30, so that the elastic modulus calculation device 30 performs the following calculation.

The elastic modulus can be calculated from the relationship regarding the bending stiffness of the fiber sample. The bending stiffness indicates the difficulty of deformation in a direction non-parallel to the direction of extension of a linearly extending member such as a beam, and is expressed as the product of the elastic modulus E of the member and the second moment of area I in the bending direction. In other words, the bending stiffness k of the hair 50 is calculated by using the elastic modulus E and the second moment of area I of the hair 50 as follows:
6 and 7, the bending stiffness k in the form of a cantilever beam is expressed as follows, using the load P applied to the other end 50b, the length L from the fixed position 50f of the hair 50 as the fiber sample to the other end 50b, and the deflection δ of the other end 50b:
Therefore, by measuring the second moment of area I of the hair 50, the load P applied to the other end 50b, the length L from the fixed position 50f of the hair 50 to the other end 50b, and the deflection δ of the other end 50b, the elastic modulus E of the hair 50 can be calculated from the relationship of this bending rigidity.

Furthermore, when a fiber sample has multiple layers, the overall bending rigidity k of the fiber sample is the sum of the bending rigidities of each layer, i.e., the sum of the product of the elastic modulus E _n and the second moment of area I _n of each layer. In other words, if the number of layers in the fiber sample is N, the bending rigidity k of the fiber sample is given by
By specifying the second moment of area and measuring the length for N or more fiber samples, the elastic modulus of each layer can be calculated from the relationship between the bending rigidity and second moment of area of each fiber sample.

The hair 50 has two layers, a cuticle 51 and a cortex 53. Therefore, the bending stiffness k is given by
Since the elastic modulus E _cu of the cuticle 51 and the elastic modulus E _co of the cortex 53 are considered to be substantially constant across a plurality of hairs 50, the elastic modulus E _cu of the cuticle 51 and the elastic modulus E _co of the cortex 53 can be calculated by specifying the second moment of area and measuring the length of two hairs 50.

The number of fiber samples for which the second moment of area is specified and the length is measured is sufficient to be the number of layers that the fiber sample has. In the above description, the elastic modulus of the hair 50 can be calculated by specifying the second moment of area and measuring the length of two hairs 50. However, by specifying the second moment of area and measuring the length of a number of fiber samples greater than the number of layers that the fiber sample has, the elastic modulus of each layer can be calculated accurately by multivariate analysis such as multiple regression analysis. That is, by specifying the second moment of area and measuring the length of three or more hairs 50, and regarding the entire bending rigidity k=E×I of the hair 50 as the objective variable, the second moment of area I _cu , I _co of each layer as the explanatory variable, the elastic modulus E _cu , E _co of each layer as the regression coefficient, and the constant term as 0, the regression coefficients E _cu , E _co can be calculated accurately.

The elastic modulus of a fiber sample is one of the factors that determine the feel (flexibility) of a fiber material. Therefore, the feel of the fiber material can be evaluated by calculating the elastic modulus of the fiber sample. In addition, in a fiber sample having multiple layers, the contribution of each layer of the fiber sample to the feel can be evaluated by calculating the elastic modulus of each layer. For example, by calculating the elastic modulus of the cuticle 51 and the cortex 53 of a person's hair 50 and comparing them with the elastic modulus of the cuticle and the cortex of a general person's hair, it can be evaluated which of the cuticle 51 and the cortex 53 contributes less to the feel, and further whether the cuticle 51 or the cortex 53 is damaged.

Next, we will explain a method for evaluating a treatment agent for a fiber material using this method for calculating the elastic modulus of a fiber sample. As an example, we will explain a method for evaluating a hair cosmetic product used to treat hair.

First, the elastic modulus of the hair 50 is calculated by the method described above. Next, the hair 50 is treated with a hair cosmetic. The hair 50 treated with the hair cosmetic is hair taken from the same subject as the hair 50 for which the elastic modulus was calculated, and is preferably the same hair as the hair 50 for which the elastic modulus was calculated. Then, the elastic modulus of the hair 50 after treatment with the hair cosmetic is calculated by the method described above. The elastic modulus of the hair 50 before treatment with the hair cosmetic is compared with the elastic modulus of the hair 50 after treatment with the hair cosmetic. This comparison allows the hair cosmetic to be evaluated. That is, the degree of contribution of the hair cosmetic to improving the feel of the hair 50 can be evaluated by the change in elastic modulus due to the hair cosmetic, in other words, the change in the feel of the hair 50 due to the hair cosmetic.

In particular, it is preferable to calculate not only the elastic modulus E of the entire hair 50 before and after treatment with the hair cosmetic, but also the elastic modulus E _cu of the cuticle 51 and the elastic modulus E _co of the cortex 53. In this case, for each layer of the hair 50, the elastic modulus of the hair 50 before treatment with the hair cosmetic is compared with the elastic modulus of the hair 50 after treatment with the hair cosmetic. The degree of contribution of the hair cosmetic to improving the feel of each layer of the hair 50 can be evaluated based on the change in the elastic modulus of each layer caused by the hair cosmetic. That is, the contribution of the hair cosmetic to the elastic modulus of the cuticle 51 and the elastic modulus of the cortex 53 of the hair 50 can be evaluated respectively.

Next, we will explain the method for manufacturing a treatment agent for textile materials based on this method for evaluating treatment agents for textile materials. As an example, we will explain below the method for manufacturing a hair cosmetic product based on the method for evaluating a hair cosmetic product.

For example, if it is determined from the results of the evaluation of the hair cosmetic described above that the hair cosmetic does not contain enough ingredients that improve the elastic modulus of the cuticle 51 of the hair 50, ingredients that improve the elastic modulus of the cuticle 51 are added to the hair cosmetic. Alternatively, if it is determined that the hair cosmetic contains too many ingredients that improve the elastic modulus of the cuticle 51 of the hair 50, the ingredients that improve the elastic modulus of the cuticle 51 are reduced in the hair cosmetic. In this way, the ingredients of the hair cosmetic are adjusted based on the results of the hair cosmetic evaluation method. This makes it possible to produce a hair cosmetic that can improve the feel, in other words, can further improve the elastic modulus.

Next, we will explain how to determine a treatment agent for a fiber material using this method for calculating the elastic modulus of a fiber sample. As an example, we will explain how to determine a hair cosmetic to be used for treating hair.

First, the hair 50 is provided by the subject. It is preferable that the number of hairs 50 provided is more than one. Next, the elastic modulus of the provided hair 50 is calculated by the above-mentioned method. Then, the hair 50 is treated with a hair cosmetic. The hair 50 treated with the hair cosmetic is preferably the same hair as the hair 50 whose elastic modulus was calculated. Then, the elastic modulus of the hair 50 after being treated with the hair cosmetic is calculated by the above-mentioned method. It is preferable to calculate not only the elastic modulus E of the entire hair 50 before and after being treated with the hair cosmetic, but also the elastic modulus E _cu of the cuticle 51 and the elastic modulus E _co of the cortex 53. The elastic modulus of the hair 50 before being treated with the hair cosmetic is compared with the elastic modulus of the hair 50 after being treated with the hair cosmetic. This makes it possible to evaluate the contribution of the hair cosmetic used in the treatment of the provided hair 50 to the change in the elastic modulus, in other words, the contribution to the change in the texture. That is, it is possible to evaluate the suitability of the hair cosmetic used to treat the provided hair 50. By treating the provided hair 50 with various hair cosmetics, it is possible to evaluate the suitability of each hair cosmetic for the provided hair 50. Based on this evaluation, it is possible to determine the optimal hair cosmetic for the subject's hair 50.

This method of determining the appropriate hair cosmetic for the hair provided in this way can be used, for example, to receive hair from a customer, determine the appropriate hair cosmetic for that hair, and sell it.

By the way, in the method of calculating the elastic modulus of a fiber sample described in Patent Document 1, the elastic modulus of the fiber sample is calculated from the relationship between the load applied to the fiber sample and the deflection of the fiber sample by measuring the deflection of the fiber sample many times while the fiber sample is under load. For this reason, many measurements are required to calculate the elastic modulus of the fiber sample, which is time-consuming. In addition, in the method of calculating the elastic modulus of a fiber sample described in Patent Document 2, the cross section of the fiber sample is measured using an atomic force microscope, and the elastic force at each cross section is evaluated by analyzing the cross section. It is not easy to observe the cross section using an atomic force microscope, and it is only possible to evaluate the local elastic force at each cross section, so it is difficult to evaluate the overall elastic modulus from the local elastic force of the fiber sample. Furthermore, in the method of calculating the elastic modulus of a fiber sample described in Non-Patent Document 2, the outer layer (cuticle) of hair as a fiber sample is scraped off with a file. It is not easy to scrape off the outer layer of hair precisely, it is time-consuming, and it may damage the fiber sample.

On the other hand, according to the method and system for calculating the elastic modulus of a fiber sample of this embodiment, the elastic modulus of the fiber sample can be calculated by one or several measurements. In addition, the second moment of area can be easily determined. Thus, in this embodiment, the elastic modulus of the fiber sample can be calculated easily because it is not time-consuming and does not require precise observation or work.

In addition, according to the method and system for calculating the elastic modulus of a fiber sample of this embodiment, the elastic modulus of the entire fiber sample can be calculated. Therefore, the feel of the entire fiber sample can be evaluated. Furthermore, according to the method for calculating the elastic modulus of a fiber sample of this embodiment, the elastic modulus of the fiber sample can be calculated without damaging the fiber sample. Therefore, the fiber sample whose elastic modulus has been calculated can be reused.

In addition, in the method and system for calculating the elastic modulus of a fiber sample according to this embodiment, the outer diameter of the fiber sample is measured. The second moment of area of the fiber sample can be easily determined from the outer diameter of the fiber sample. Therefore, the elastic modulus of the fiber sample can be easily calculated. The feel of the fiber sample can be evaluated from the elastic modulus of the fiber sample.

Furthermore, according to the method and system for calculating the elastic modulus of a fiber sample of this embodiment, when the fiber sample has multiple layers made of different materials, the thickness of each layer of the fiber sample is measured. The second moment of area of each layer of the fiber sample can be easily determined from the outer diameter of the fiber sample and the thickness of each layer. Therefore, the elastic modulus of each layer of the fiber sample can be easily calculated. The contribution of each layer of the fiber sample to the feel can be evaluated from the elastic modulus of each layer.

In addition, the number of fiber samples prepared is greater than the number of layers that the fiber sample has. By determining the second moment of area and measuring the length of a greater number of fiber samples than the number of layers that the fiber sample has, the elastic modulus of each layer can be calculated with high accuracy using multivariate analysis. In other words, the contribution of each layer of the fiber sample to the feel can be evaluated with high accuracy.

Furthermore, in the method for evaluating hair cosmetics of this embodiment, the elastic modulus of the hair 50 can be calculated without damaging the hair 50, so that the elastic modulus of the same hair 50 can be compared before and after treatment with the hair cosmetic. This allows for a more appropriate evaluation of the change in the elastic modulus of the hair 50 caused by the hair cosmetic.

The method for producing hair cosmetics in this embodiment adjusts the ingredients of the hair cosmetics based on such evaluations of the hair cosmetics. This makes it possible to produce hair cosmetics that can appropriately improve the elastic modulus.

In the method for determining a hair cosmetic product according to the present embodiment, the elastic modulus of the hair 50 can be calculated without damaging the hair 50, so that the elastic modulus of the same hair 50 can be compared before and after treatment with a hair cosmetic product. This allows for a more appropriate evaluation of the suitability of the hair cosmetic product for the hair 50.

As described above, the method for calculating the elastic modulus of a fiber sample according to the present embodiment includes a step of determining the second moment of area of the fiber sample, a step of measuring the length L between the fixing position 50f and the other end 50b of the fiber sample and the deflection amount δ of the other end 50b while fixing only one end 50a of the fiber sample and applying a predetermined load to the other end 50b, and a step of calculating the elastic modulus of the fiber sample from the second moment of area I of the fiber sample, the length L between the fixing position 50f and the other end 50b of the fiber sample, and the deflection amount δ of the other end 50b. According to this method for calculating the elastic modulus of a fiber sample, the elastic modulus of the fiber sample can be calculated from the second moment of area, which is easily determined, and the length L between the fixing position 50f and the other end 50b of the fiber sample, which is easily measured, and the deflection amount δ of the other end 50b. These values can be easily determined or measured, so that the elastic modulus of the fiber sample can be easily calculated.

In addition, the method for calculating the elastic modulus of a fiber sample in this embodiment is a method for calculating the elastic modulus of each layer of a fiber sample having multiple layers made of different materials, and includes the steps of: preparing multiple fiber samples taken from the same subject, the number of fiber samples being equal to or greater than the number of layers the fiber sample has; identifying the second moment of area of each layer of each fiber sample; measuring, for each fiber sample, the length L between the fixed position 50f and the other end 50b of the fiber sample and the deflection amount δ of the other end 50b while fixing only one end 50a of the fiber sample and applying a predetermined load to the other end 50b; and calculating the elastic modulus of each layer of the fiber sample from the second moment of area of each fiber sample, the length L between the fixed position 50f and the other end 50b of the fiber sample, and the deflection amount δ of the other end 50b. According to this method for calculating the elastic modulus of a fiber sample, the elastic modulus of each layer of the fiber sample can be calculated from the easily identified second moment of area of each layer, the easily measured length L between the fixed position 50f and the other end 50b of each fiber sample, and the deflection amount δ of the other end 50b. Because these values can be easily identified or measured, the elastic modulus of each layer of the fiber sample can be easily calculated.

Note that various modifications can be made to this embodiment.

For example, in the above-described embodiment, the length (deflection) δ of the other end 50b of the hair 50 is measured by comparing the state before and after the load P is applied to the other end 50b of the hair 50. However, the length (deflection) δ of the other end 50b of the hair 50 may also be measured by comparing the state in which a load P1 is applied to the other end 50b of the hair 50 with the state in which a load P2 is applied. In this case, the bending stiffness k of the hair 50 can be calculated by using the difference between the load P1 and the load P2 instead of the load P.

The hair 50 can bend not only due to the load applied to the other end 50b, but also due to the weight of the hair 50 itself. Therefore, when measuring the length (deflection) δ of the other end 50b of the hair 50 by comparing the state before and after the load P is applied to the other end 50b of the hair 50, the sum of the deflection due to the load P and the deflection due to the weight of the hair 50 is measured. For this reason, it is difficult to measure the deflection due to the load P alone. On the other hand, when comparing the state in which the load P1 is applied to the other end 50b of the hair 50 with the state in which the load P2 is applied, the influence of the weight of the hair 50 can be eliminated in the relationship between the difference between the load P1 and the load P2 and the deflection δ of the other end 50b. Therefore, the relationship between the load and the deflection of the other end 50b can be measured more accurately. In other words, the elastic modulus of the hair 50 can be calculated more accurately.

The present invention will be described in more detail below using examples, but the present invention is not limited to these examples.

Subject A provided ten hairs A1 to A10 as fiber samples. A part of each hair was cut to expose the cut surface, and the cut surface was observed under a microscope (Keyence Corporation laser microscope VK-X250). From the image of the observed cut surface, the major axis a, minor axis b, and cuticle thickness D ₁ of each hair were measured. From these values, the area moment of inertia I of each hair, the area moment of inertia I _cu of the cuticle, and the area moment of inertia I _co of the cortex were calculated. Then, for each hair, only one end side was fixed, and a load of 1 mg weight was applied to the other end. The deflection amount δ of the other end was measured by comparing the image taken before the load was applied and the image taken after the load was applied. In addition, the length L between the fixed position of the hair and the other end was measured. From these measurement results, the elastic modulus E of each hair was calculated.

For each of the hairs A1 to A10, the measured major axis a, minor axis b, cuticle thickness D ₁ , length L between the fixed position of the hair and the other end, deflection δ at the other end, second moment of area I, second moment of area I _cu of the cuticle, and second moment of area I _co of the cortex, as well as the calculated elastic modulus E, are shown in Table 1 below.

The elastic modulus of the cuticle E cu and the elastic modulus of the cortex E co can be calculated by multiple regression analysis using E x I = E _cu x I _cu + E _co x I _co based on the results of the area second moment _I , the elastic modulus of the hair, the area second moment I _cu and the area second moment I _co of the cortex for each of the hairs A1 to A10 shown in Table 1. Specifically, by considering the multiple regression equation with E x I as the objective variable, the _area second moments I _cu and I _co as explanatory variables, the elastic modulus E _cu and E _co as regression coefficients, and the constant term being 0, the elastic modulus of the cuticle E _cu is calculated to be 15.62 GPa, and the elastic modulus of the cortex E _co as 0.86 GPa.

In this way, the elastic modulus of the fiber sample and the elastic modulus of each layer of the fiber sample can be easily calculated.

1 System for calculating elastic modulus of fiber sample 10 Second moment of area determination device 20 Length measurement device 30 Elastic modulus calculation device 50 Hair 50a One end 50b Other end 50f Fixation position 51 Cuticle 53 Cortex 55 Medulla

Claims (7)

1. A method for calculating the elastic modulus of each layer of a textile sample having multiple layers of different materials, comprising the steps of:
preparing a number of fiber samples taken from the same subject, the number of fiber samples being equal to or greater than the number of layers in the fiber sample;
Identifying the second moment of area of each layer of each fiber sample;
a step of measuring, for each fiber sample, a length between a fixing position of the fiber sample and the other end and a deflection amount of the other end while fixing only one end of the fiber sample and applying a predetermined load to the other end;
A method for calculating the elastic modulus of a fiber sample, comprising a step of calculating the elastic modulus of each layer of the fiber sample from the second moment of area of each fiber sample, the length between the fixed position and the other end of the fiber sample, and the deflection amount of the other end. The method for calculating the elastic modulus of a fiber sample according to claim 1 , wherein the step of determining the second moment of area of each layer includes the step of measuring an outer diameter of the fiber sample and a thickness of each layer. The method for calculating the elastic modulus of a fiber sample according to claim 1 or 2 , wherein in the step of preparing the fiber sample, the number of the fiber samples prepared is greater than the number of layers that the fiber sample has. The method for calculating the elastic modulus of a fiber sample according to claim 1 , wherein the fiber sample is mammalian body hair. Calculating the elastic modulus of the hair by the method for calculating the elastic modulus of a fiber sample according to any one of claims 1 to 4 ;
treating the hair with a hair cosmetic;
calculating the elastic modulus of the hair after the treatment with the hair cosmetic composition by the method for calculating the elastic modulus of a fiber sample according to any one of claims 1 to 4 ;
and comparing the elastic modulus of the hair before treatment with the hair cosmetic product with the elastic modulus of the hair after treatment with the hair cosmetic product. A method for producing a hair cosmetic, comprising a step of adjusting ingredients of the hair cosmetic based on the method for evaluating a hair cosmetic according to claim 5 . Receiving a donation of hair;
Calculating the elastic modulus of the provided hair by the method for calculating the elastic modulus of a fiber sample according to any one of claims 1 to 4 ;
treating the hair with a hair cosmetic;
calculating the elastic modulus of the hair after the treatment with the hair cosmetic composition by the method for calculating the elastic modulus of a fiber sample according to any one of claims 1 to 4 ;
and evaluating the suitability of the hair cosmetic for the provided hair by comparing the elastic modulus of the hair before treatment with the hair cosmetic and the elastic modulus of the hair after treatment with the hair cosmetic.